(************** Content-type: application/mathematica **************

                    Mathematica-Compatible Notebook

This notebook can be used with any Mathematica-compatible
application, such as Mathematica, MathReader or Publicon. The data
for the notebook starts with the line containing stars above.

To get the notebook into a Mathematica-compatible application, do
one of the following:

* Save the data starting with the line of stars above into a file
  with a name ending in .nb, then open the file inside the
  application;

* Copy the data starting with the line of stars above to the
  clipboard, then use the Paste menu command inside the application.

Data for notebooks contains only printable 7-bit ASCII and can be
sent directly in email or through ftp in text mode.  Newlines can be
CR, LF or CRLF (Unix, Macintosh or MS-DOS style).

NOTE: If you modify the data for this notebook not in a Mathematica-
compatible application, you must delete the line below containing
the word CacheID, otherwise Mathematica-compatible applications may
try to use invalid cache data.

For more information on notebooks and Mathematica-compatible 
applications, contact Wolfram Research:
  web: http://www.wolfram.com
  email: info@wolfram.com
  phone: +1-217-398-0700 (U.S.)

Notebook reader applications are available free of charge from 
Wolfram Research.
*******************************************************************)

(*CacheID: 232*)


(*NotebookFileLineBreakTest
NotebookFileLineBreakTest*)
(*NotebookOptionsPosition[    101490,       3525]*)
(*NotebookOutlinePosition[    102639,       3559]*)
(*  CellTagsIndexPosition[    102595,       3555]*)
(*WindowFrame->Normal*)



Notebook[{

Cell[CellGroupData[{
Cell["Die Anordnung der reellen Zahlen", "Section"],

Cell[TextData[{
  "Materialien zur Vorlesung ",
  StyleBox["Elementare Analysis",
    FontWeight->"Bold"],
  ", Wintersemester 2003 / 4"
}], "SmallText"],

Cell["\<\

Wenn Sie sich die reellen Zahlen als Punkte auf einer Zahlengerade \
vorstellen, ist es sinnvoll erst einmal zwei Stellen zu fixieren f\
\[UDoubleDot]r Null und Eins:\
\>", "Text",
  FontFamily->"Times New Roman"],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: .1 
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% Graphics
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12  scalefont  setfont
% Scaling calculations
0.101874 0.78064 0.0568027 2.72109 [
[ 0 0 0 0 ]
[ 1 .1 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .1 L
0 .1 L
closepath
clip
newpath
% Start of user PostScript
/mathtops {
gsave
MBeginOrig
moveto
MEndOrig
currentpoint
grestore
} bind def
/MAtocoords {
mathtops 4 2 roll mathtops
4 copy pop pop
3 -1 roll sub
/arry exch def
exch sub
/arrx exch def
arrx dup mul
arry dup mul
add sqrt
/arrl exch def
translate
} bind def
/MAarrowhead1 {
gsave
MAtocoords
arrl 0. eq
{ 0 0 Mdot }
{
[ arrx arrl div
arry arrl div
-1 arry mul arrl div
arrx arrl div
0 0 ]
concat
-0.04 0.01 moveto 0 0 lineto
-0.04 -0.01 lineto
-0.02 0 lineto fill
-0.04 0.01 moveto 0 0 lineto
-0.04 -0.01 lineto
-0.02 0 lineto
-0.04 0.01 lineto stroke
} ifelse
grestore
} def
% End of user PostScript
0 g
1.5 Mabswid
[ ] 0 setdash
.02381 .0568 m
.96058 .0568 L
s
.02381 .0568 m
.97619 .0568 L
s
% Start of user PostScript
-0.1 0 1.12 0 MAarrowhead1
% End of user PostScript
.9 Mabswid
.10187 .07041 m
.10187 .0432 L
s
.88251 .07041 m
.88251 .0432 L
s
gsave
.10187 .01599 -66 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0) show
69.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
gsave
.88251 .01599 -66 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(1) show
69.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  ImageSize->{378.25, 37.5625},
  ImageMargins->{{43, 0}, {0, 0}},
  ImageRegion->{{0, 1}, {0, 1}},
  FontFamily->"Times New Roman",
  ImageCache->GraphicsData["Bitmap", "\<\
CF5dJ6E]HGAYHf4PAg9QL6QYHg<PAVmbKF5d0`40005j00009A000`40O003h00OogooNgoo003oOomk
Ool00?moog]oo`00:Goo0`00ogoo6goo0`00<Goo000XOol01@00Oomoogoo0000ogoo6goo00<007oo
Ool0<7oo000XOol01@00Oomoogoo0000ogoo6goo00<007ooOol0<7oo000XOol01@00Oomoogoo0000
ogoo6goo00<007ooOol0<7oo000XOol01@00Oomoogoo0000ogoo6goo00<007ooOol0<7oo000XOol0
1@00Oomoogoo0000ogoo6goo00<007ooOol0<7oo000XOol01@00Oomoogoo0000ogoo6goo00<007oo
Ool0<7oo000XOol01@00Oomoogoo0000ogoo6Woo0P00<Woo000YOol3003oOolLOol00`00Oomoo`0`
Ool00?moog]oo`00ogooNgoo003oOomkOol00?moog]oo`00:goo00<007ooOol0ogoo6goo00<007oo
Ool0;goo000[Ool00`00Oomoo`3oOolKOol00`00Oomoo`0AOol2000LOol002]oo`03001oogoo0?mo
oa]oo`03001oogoo019oo`D001Qoo`00:goo00<007ooOol0ogoo6goo00<007ooOol057oo1P005Goo
000[Ool00`00Oomoo`3oOolKOol00`00Oomoo`0FOol8000AOol000ioool005h000moo`00:goo00<0
07ooOol0ogoo6goo00<007ooOol05Goo20004Woo000[Ool00`00Oomoo`3oOolKOol00`00Oomoo`0C
Ool6000FOol002]oo`03001oogoo0?mooa]oo`03001oogoo015oo`<001]oo`00:goo00<007ooOol0
ogoo6goo00<007ooOol0;goo000[Ool00`00Oomoo`3oOolKOol00`00Oomoo`0_Ool00?moog]oo`00
ogooNgoo003oOomkOol00?moog]oo`00ogooNgoo003oOomkOol00?moog]oo`00ogooNgoo003oOomk
Ool00?moog]oo`00\
\>"],
  ImageRangeCache->{{{90.625, 392.188}, {233, 204}} -> {-0.556361, 0.237645, \
0.00353383, 0.0010138}}],

Cell[TextData[{
  "Ist dann  ",
  Cell[BoxData[
      \(TraditionalForm\`a \[Element] \ \[DoubleStruckCapitalR]\)]],
  " und  ",
  Cell[BoxData[
      \(TraditionalForm\`a \[NotEqual] 0\)]],
  " , so liegt  ",
  StyleBox["a",
    FontSlant->"Italic"],
  "  rechts bzw. links von Null auf der Zahlengerade.  \[Dash]",
  StyleBox["a",
    FontSlant->"Italic"],
  "  liegt in jedem Fall auf der jeweils anderen Seite."
}], "Text",
  FontFamily->"Times New Roman"],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: .3 
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% Graphics
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12  scalefont  setfont
% Scaling calculations
0.142857 0.595238 0.239286 0.0357143 [
[.14286 .18571 -8.84375 -7.84375 ]
[.14286 .18571 8.84375 7.84375 ]
[.44048 .18571 -5 -7.84375 ]
[.44048 .18571 5 7.84375 ]
[.7381 .18571 -5 -7.84375 ]
[.7381 .18571 5 7.84375 ]
[.14286 .025 -5 -7.84375 ]
[.14286 .025 5 7.84375 ]
[.44048 .025 -5 -7.84375 ]
[.44048 .025 5 7.84375 ]
[.7381 .025 -8.84375 -7.84375 ]
[.7381 .025 8.84375 7.84375 ]
[.97619 .18571 0 -7.84375 ]
[.97619 .18571 36.625 7.84375 ]
[.97619 .18571 -13 -7.84375 ]
[.97619 .18571 0 7.84375 ]
[.97619 .025 0 -7.84375 ]
[.97619 .025 42 7.84375 ]
[.97619 .025 -13 -7.84375 ]
[.97619 .025 0 7.84375 ]
[ 0 0 0 0 ]
[ 1 .3 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
% Start of user PostScript
/mathtops {
gsave
MBeginOrig
moveto
MEndOrig
currentpoint
grestore
} bind def
/MAtocoords {
mathtops 4 2 roll mathtops
4 copy pop pop
3 -1 roll sub
/arry exch def
exch sub
/arrx exch def
arrx dup mul
arry dup mul
add sqrt
/arrl exch def
translate
} bind def
/MAarrowhead1 {
gsave
MAtocoords
arrl 0. eq
{ 0 0 Mdot }
{
[ arrx arrl div
arry arrl div
-1 arry mul arrl div
arrx arrl div
0 0 ]
concat
-0.04 0.01 moveto 0 0 lineto
-0.04 -0.01 lineto
-0.02 0 lineto fill
-0.04 0.01 moveto 0 0 lineto
-0.04 -0.01 lineto
-0.02 0 lineto
-0.04 0.01 lineto stroke
} ifelse
grestore
} def
% End of user PostScript
0 g
1.5 Mabswid
[ ] 0 setdash
.02381 .23929 m
.85714 .23929 L
s
.08333 .23929 m
.86905 .23929 L
s
% Start of user PostScript
-0.1 0 1.22 0 MAarrowhead1
% End of user PostScript
.9 Mabswid
.14286 .25714 m
.14286 .22143 L
s
.44048 .25714 m
.44048 .22143 L
s
.7381 .25714 m
.7381 .22143 L
s
gsave
.14286 .18571 -69.8438 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Math1
%%IncludeFont: Math1
/Math1 findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(-) show
70.688 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(a) show
76.688 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
gsave
.44048 .18571 -66 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0) show
69.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
gsave
.7381 .18571 -66 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(a) show
69.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
1.5 Mabswid
.02381 .09643 m
.85714 .09643 L
s
.08333 .09643 m
.86905 .09643 L
s
% Start of user PostScript
-0.1 -4. 1.22 -4. MAarrowhead1
% End of user PostScript
.9 Mabswid
.14286 .11429 m
.14286 .07857 L
s
.44048 .11429 m
.44048 .07857 L
s
.7381 .11429 m
.7381 .07857 L
s
gsave
.14286 .025 -66 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(a) show
69.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
gsave
.44048 .025 -66 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0) show
69.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
gsave
.7381 .025 -69.8438 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Math1
%%IncludeFont: Math1
/Math1 findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(-) show
70.688 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(a) show
76.688 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
gsave
.97619 .18571 -61 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(positiv) show
95.625 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
gsave
.97619 .18571 -74 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(a) show
72.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
gsave
.97619 .025 -61 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
66.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(negativ) show
101.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
gsave
.97619 .025 -74 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(a) show
72.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
0 0 m
1 0 L
1 .3 L
0 .3 L
closepath
clip
newpath
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  ImageSize->{441.625, 132.313},
  ImageMargins->{{46.3125, 0}, {0, 0}},
  ImageRegion->{{0, 1}, {0, 1}},
  FontFamily->"Times New Roman",
  ImageCache->GraphicsData["Bitmap", "\<\
CF5dJ6E]HGAYHf4PAg9QL6QYHg<PAVmbKF5d0`40006i0000Q1000`40O003h00Oogoo^Woo003oOonj
Ool00?mookYoo`00ogoo^Woo003oOonjOol00?mookYoo`00ogoo^Woo003oOonjOol00?mookYoo`00
ogooX7oo0`005goo003oOonOOol01@00Oomoogoo00005Woo003oOonOOol01@00Oomoogoo00005Woo
000gOol200000goo0000001eOol3001jOol200000goo0000001@Ool200000goo0000000;Ool30000
17oo000007oo0P000goo0`000Woo100000Aoo`00001oo`<0009oo`03001oogoo00Eoo`00=goo00@0
07oo000007Eoo`05001oogooOol0001iOol01000Ool00000DGoo00@007oo000000eoo`06001oogoo
001oo`000Woo00<007oo000017oo00@007ooOol0009oo`05001oogooOol00003Ool00`00Oomoo`05
Ool003Moo`04001oogoo001eOol01@00Oomoogoo0000NGoo00@007ooOol0055oo`04001oogoo000=
Ool01P00Oomoo`00Ool000Eoo`80009oo`04001oogoo0002Ool01@00Oomoogoo00000Woo00<007oo
00001Woo000gOol01@00Oomoogoo0000M7oo00D007ooOomoo`00079oo`P000=oo`03001oogoo04io
o`05001oogooOol0000<Ool01@00Oomoo`00Ool0100000Eoo`00Oomoo`00009oo`<0009oo`05001o
ogooOol00002Ool00`00Ool00006Ool003Qoo`04001oogoo001dOol01@00Oomoogoo0000NWoo00@0
07ooOol0055oo`04001oogoo000<Ool2000017oo001oo`000Woo00<007oo00000Woo00<007oo0000
0Woo00@007ooOol000=oo`03001oo`0000=oo`03001oogoo00=oo`00>Goo0`00M7oo00D007ooOomo
o`0007]oo`<0059oo`<000]oo`800003Ool007oo009oo`8000=oo`@00003Ool00000009oo`<00003
Ool0000000<0009oo`8000Aoo`00/7oo00D007ooOomoo`000?Aoo`03001oogoo00eoo`00/7oo00D0
07ooOomoo`000?Aoo`03001oogoo00eoo`00/Goo0`00nGoo00<007ooOol02Goo003oOonjOol00?mo
okYoo`00ogoo^Woo003oOonjOol00?mookYoo`00ogoo^Woo003oOonjOol00?mookYoo`00ogoo^Woo
003oOonjOol00?mookYoo`00ogoo^Woo003oOonjOol00?mookYoo`00ogoo^Woo003oOonjOol003Yo
o`03001oogoo07Ioo`03001oogoo07Moo`03001oogoo08Uoo`00>Woo00<007ooOol0MWoo00<007oo
Ool0Mgoo00<007ooOol0RGoo000jOol00`00Oomoo`1fOol00`00Oomoo`1gOol00`00Oomoo`29Ool0
03Yoo`03001oogoo07Ioo`03001oogoo07Moo`03001oogoo029oo`8006Eoo`00>Woo00<007ooOol0
MWoo00<007ooOol0Mgoo00<007ooOol08goo1@00HGoo000jOol00`00Oomoo`1fOol00`00Oomoo`1g
Ool00`00Oomoo`0UOol7001MOol003Yoo`03001oogoo07Ioo`03001oogoo07Moo`03001oogoo02Mo
o`T005Uoo`002Gooo`00F`00EWoo000jOol00`00Oomoo`1fOol00`00Oomoo`1gOol00`00Oomoo`0X
Ool9001HOol003Yoo`03001oogoo07Ioo`03001oogoo07Moo`03001oogoo02Ioo`L005aoo`00>Woo
00<007ooOol0MWoo00<007ooOol0Mgoo00<007ooOol097oo1@00H7oo000jOol00`00Oomoo`1fOol0
0`00Oomoo`1gOol00`00Oomoo`0ROol3001TOol003Yoo`03001oogoo07Ioo`03001oogoo07Moo`03
001oogoo08Uoo`00>Woo00<007ooOol0MWoo00<007ooOol0Mgoo00<007ooOol0RGoo000jOol00`00
Oomoo`1fOol00`00Oomoo`1gOol00`00Oomoo`29Ool00?mookYoo`00ogoo^Woo003oOonjOol00?mo
okYoo`00ogoo^Woo003oOonjOol00?mookYoo`00ogoo^Woo003oOonjOol00?mookYoo`00ogoo^Woo
003oOonjOol00?mookYoo`00ogoo^Woo003oOonjOol00?mookYoo`00ogoo^Woo003oOonjOol00?mo
okYoo`00ogoo^Woo003oOonjOol00?mookYoo`00ogooTGoo0`009Woo003oOonBOol00`00Oomoo`0U
Ool00?mooi9oo`03001oogoo02Eoo`00>goo0P0000=oo`000000LGoo0`00MWoo0P0000=oo`000000
E7oo0P0000=oo`0000002Goo00@007oo000000=oo`<0009oo`<0009oo`<00004Ool00000Ool30002
Ool00`00Oomoo`08Ool003]oo`04001oo`00001aOol01@00Oomoogoo0000MGoo00@007oo000005Eo
o`04001oo`00000:Ool20002Ool00`00Ool00003Ool00`00Ool00002Ool01000Oomoo`000Woo00D0
07ooOomoo`0000=oo`03001oogoo00Qoo`00>goo00@007ooOol0075oo`05001oogooOol0001eOol0
1000Oomoo`00EGoo00@007ooOol000Yoo`07001oogooOol007oo00000goo00@007ooOomoo`80009o
o`04001oogoo0003Ool01P00Oomoo`00Ool000Uoo`00=7oo20000goo00<007ooOol0KWoo00D007oo
Oomoo`0007Eoo`05001oogooOol0001DOol01@00Oomoogoo00002Goo00L007ooOomoo`00Ool00003
Ool01000Ool0000017oo00@007ooOol000=oo`06001oogoo001oo`002Goo000lOol01000Oomoo`00
L7oo00D007ooOomoo`0007Ioo`04001oogoo001EOol01000Oomoo`002Goo0P000Woo00<007oo0000
0goo00<007oo00000Woo00@007ooOol0009oo`07001oogooOol007oo00000goo00<007ooOol01Woo
000mOol3001`Ool01@00Oomoogoo0000Mgoo0`00EWoo0`0027oo0P0000=oo`0000000goo0`000goo
0`0000Aoo`00001oo`<00003Ool0000000<0009oo`8000Moo`00/7oo00D007ooOomoo`000?5oo`03
001oogoo011oo`00/7oo00D007ooOomoo`000?5oo`03001oogoo011oo`00/Goo0`00kgoo00<007oo
Ool017oo00<007ooOol037oo003oOonjOol00?mookYoo`00ogoo^Woo003oOonjOol00?mookYoo`00
ogoo^Woo003oOonjOol00?mookYoo`00ogoo^Woo000jOol00`00Oomoo`1fOol00`00Oomoo`1gOol0
0`00Oomoo`29Ool003Yoo`03001oogoo07Ioo`03001oogoo07Moo`03001oogoo08Uoo`00>Woo00<0
07ooOol0MWoo00<007ooOol0Mgoo00<007ooOol0RGoo000jOol00`00Oomoo`1fOol00`00Oomoo`1g
Ool00`00Oomoo`0ROol2001UOol003Yoo`03001oogoo07Ioo`03001oogoo07Moo`03001oogoo02=o
o`D0065oo`00>Woo00<007ooOol0MWoo00<007ooOol0Mgoo00<007ooOol09Goo1`00GGoo000jOol0
0`00Oomoo`1fOol00`00Oomoo`1gOol00`00Oomoo`0WOol9001IOol000Uoool005/005Ioo`00>Woo
00<007ooOol0MWoo00<007ooOol0Mgoo00<007ooOol0:7oo2@00F7oo000jOol00`00Oomoo`1fOol0
0`00Oomoo`1gOol00`00Oomoo`0VOol7001LOol003Yoo`03001oogoo07Ioo`03001oogoo07Moo`03
001oogoo02Aoo`D0061oo`00>Woo00<007ooOol0MWoo00<007ooOol0Mgoo00<007ooOol08Woo0`00
I7oo000jOol00`00Oomoo`1fOol00`00Oomoo`1gOol00`00Oomoo`29Ool003Yoo`03001oogoo07Io
o`03001oogoo07Moo`03001oogoo08Uoo`00>Woo00<007ooOol0MWoo00<007ooOol0Mgoo00<007oo
Ool0RGoo000jOol00`00Oomoo`1fOol00`00Oomoo`1gOol00`00Oomoo`29Ool00?mookYoo`00ogoo
^Woo003oOonjOol00?mookYoo`00ogoo^Woo003oOonjOol00?mookYoo`00ogoo^Woo003oOonjOol0
0?mookYoo`00ogoo^Woo003oOonjOol00?mookYoo`00ogoo^Woo003oOonjOol00?mookYoo`00ogoo
^Woo003oOonjOol00?mookYoo`00ogoo^Woo003oOonjOol00001\
\>"],
  ImageRangeCache->{{{93.25, 445.5}, {385.688, 280.875}} -> {-0.719944, \
17.0979, 0.00411741, 0.0686235}}],

Cell[TextData[{
  "Liegen  ",
  Cell[BoxData[
      \(TraditionalForm\`a, b \[Element] \ \[DoubleStruckCapitalR]\)]],
  "  rechts von Null, so auch ihre Summe  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " + ",
  StyleBox["b",
    FontSlant->"Italic"],
  "  und ihr Produkt  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " \[CenterDot] ",
  StyleBox["b",
    FontSlant->"Italic"],
  " ."
}], "Text",
  FontFamily->"Times New Roman"],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: .1 
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% Graphics
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12  scalefont  setfont
% Scaling calculations
0.157948 0.670691 0.0568027 0.0272109 [
[ 0 0 0 0 ]
[ 1 .1 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .1 L
0 .1 L
closepath
clip
newpath
% Start of user PostScript
/mathtops {
gsave
MBeginOrig
moveto
MEndOrig
currentpoint
grestore
} bind def
/MAtocoords {
mathtops 4 2 roll mathtops
4 copy pop pop
3 -1 roll sub
/arry exch def
exch sub
/arrx exch def
arrx dup mul
arry dup mul
add sqrt
/arrl exch def
translate
} bind def
/MAarrowhead1 {
gsave
MAtocoords
arrl 0. eq
{ 0 0 Mdot }
{
[ arrx arrl div
arry arrl div
-1 arry mul arrl div
arrx arrl div
0 0 ]
concat
-0.04 0.01 moveto 0 0 lineto
-0.04 -0.01 lineto
-0.02 0 lineto fill
-0.04 0.01 moveto 0 0 lineto
-0.04 -0.01 lineto
-0.02 0 lineto
-0.04 0.01 lineto stroke
} ifelse
grestore
} def
% End of user PostScript
0 g
1.5 Mabswid
[ ] 0 setdash
.02381 .0568 m
.96278 .0568 L
s
.09088 .0568 m
.97619 .0568 L
s
% Start of user PostScript
-0.1 0 1.22 0 MAarrowhead1
% End of user PostScript
.9 Mabswid
.15795 .07041 m
.15795 .0432 L
s
.42622 .07041 m
.42622 .0432 L
s
.15795 .07041 m
.15795 .0432 L
s
.56036 .07041 m
.56036 .0432 L
s
.82864 .07041 m
.82864 .0432 L
s
gsave
.15795 .01599 -66 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0) show
69.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
gsave
.42622 .01599 -66 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(b) show
69.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
gsave
.56036 .01599 -66 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(a) show
69.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
gsave
.82864 .01599 -75.8438 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(a) show
72.000 15.813 moveto
%%IncludeResource: font Math1
%%IncludeFont: Math1
/Math1 findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(+) show
82.688 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(b) show
88.688 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  ImageSize->{370.625, 36.9375},
  ImageMargins->{{43, 0}, {0, 0}},
  ImageRegion->{{0, 1}, {0, 1}},
  FontFamily->"Times New Roman",
  ImageCache->GraphicsData["Bitmap", "\<\
CF5dJ6E]HGAYHf4PAg9QL6QYHg<PAVmbKF5d0`40005b000091000`40O003h00OogooLgoo003oOomc
Ool003]oo`<005ioo`8002eoo`800003Ool00000059oo`800003Ool0000000Qoo`03001oogoo00Ao
o`8003Yoo`00>Woo00D007ooOomoo`0005aoo`04001oogoo000/Ool01000Ool00000Dgoo00@007oo
000000Uoo`03001oogoo00=oo`04001oogoo000iOol003Yoo`05001oogooOol0001LOol01@00Oomo
ogoo0000:goo00@007ooOol005=oo`04001oogoo0009Ool00`00Oomoo`03Ool01@00Oomoogoo0000
>7oo000jOol01@00Oomoogoo0000GGoo00@007ooOol002]oo`05001oogooOol0001BOol01@00Oomo
ogoo00001Goo1`000goo00@007ooOol003Qoo`00>Woo00D007ooOomoo`0005eoo`800003Ool007oo
02]oo`04001oogoo001COol01000Oomoo`0027oo00<007ooOol017oo0P0000=oo`00Ool0=goo000j
Ool01@00Oomoogoo0000GGoo00@007oo000002eoo`<005Aoo`<000Qoo`03001oogoo00Aoo`04001o
o`00000hOol003Yoo`05001oogooOol0001MOol00`00Oomoo`2@Ool00`00Oomoo`04Ool00`00Oomo
o`0iOol003Yoo`05001oogooOol0001NOol00`00Oomoo`2GOol00`00Oomoo`0hOol003]oo`<005io
o`8009Qoo`8003Yoo`00ogooLgoo003oOomcOol00?moog=oo`00ogooLgoo000mOol00`00Oomoo`1N
Ool00`00Oomoo`0]Ool00`00Oomoo`1MOol00`00Oomoo`11Ool003eoo`03001oogoo05ioo`03001o
ogoo02eoo`03001oogoo05eoo`03001oogoo02Aoo`8001]oo`00?Goo00<007ooOol0GWoo00<007oo
Ool0;Goo00<007ooOol0GGoo00<007ooOol09Goo1@005goo000mOol00`00Oomoo`1NOol00`00Oomo
o`0]Ool00`00Oomoo`1MOol00`00Oomoo`0WOol6000DOol003eoo`03001oogoo05ioo`03001oogoo
02eoo`03001oogoo05eoo`03001oogoo02Uoo`P0011oo`003Gooo`00F0003Woo000mOol00`00Oomo
o`1NOol00`00Oomoo`0]Ool00`00Oomoo`1MOol00`00Oomoo`0YOol8000@Ool003eoo`03001oogoo
05ioo`03001oogoo02eoo`03001oogoo05eoo`03001oogoo02Moo`H001Aoo`00?Goo00<007ooOol0
GWoo00<007ooOol0;Goo00<007ooOol0GGoo00<007ooOol09Goo1@005goo000mOol00`00Oomoo`1N
Ool00`00Oomoo`0]Ool00`00Oomoo`1MOol00`00Oomoo`0TOol2000KOol003eoo`03001oogoo05io
o`03001oogoo02eoo`03001oogoo05eoo`03001oogoo045oo`00ogooLgoo003oOomcOol00?moog=o
o`00ogooLgoo003oOomcOol00?moog=oo`00ogooLgoo003oOomcOol00?moog=oo`00ogooLgoo0000
\
\>"],
  ImageRangeCache->{{{90.625, 386.125}, {447.813, 419.313}} -> {-0.73709, \
51.9822, 0.0041853, 0.103159}}],

Cell[TextData[{
  StyleBox["a",
    FontSlant->"Italic"],
  " \[CenterDot] ",
  StyleBox["b",
    FontSlant->"Italic"],
  "  k\[ODoubleDot]nnen Sie sich als Ma\[SZ]zahl des \
Fl\[ADoubleDot]cheninhaltes eines Rechteckes mit den Seiten der \
L\[ADoubleDot]ngen  ",
  StyleBox["a",
    FontSlant->"Italic"],
  "  und  ",
  StyleBox["b",
    FontSlant->"Italic"],
  "  vorstellen.\nWenn Sie sich eine reelle Zahl  ",
  StyleBox["a",
    FontSlant->"Italic"],
  "  denken, dann k\[ODoubleDot]nnen Sie beim \"Durchlaufen\" der nat\
\[UDoubleDot]rlichen Zahlen auf dem Zahlenstrahl immer eine \
nat\[UDoubleDot]rliche Zahl  ",
  StyleBox["n",
    FontSlant->"Italic"],
  "  finden, die rechts von  ",
  StyleBox["a",
    FontSlant->"Italic"],
  "  liegt:\n"
}], "Text",
  FontFamily->"Times New Roman"],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: .12 
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% Graphics
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12  scalefont  setfont
% Scaling calculations
0.0959596 0.721501 0.0681633 0.0326531 [
[ 0 0 0 0 ]
[ 1 .12 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 0 m
1 0 L
1 .12 L
0 .12 L
closepath
clip
newpath
% Start of user PostScript
/mathtops {
gsave
MBeginOrig
moveto
MEndOrig
currentpoint
grestore
} bind def
/MAtocoords {
mathtops 4 2 roll mathtops
4 copy pop pop
3 -1 roll sub
/arry exch def
exch sub
/arrx exch def
arrx dup mul
arry dup mul
add sqrt
/arrl exch def
translate
} bind def
/MAarrowhead1 {
gsave
MAtocoords
arrl 0. eq
{ 0 0 Mdot }
{
[ arrx arrl div
arry arrl div
-1 arry mul arrl div
arrx arrl div
0 0 ]
concat
-0.04 0.01 moveto 0 0 lineto
-0.04 -0.01 lineto
-0.02 0 lineto fill
-0.04 0.01 moveto 0 0 lineto
-0.04 -0.01 lineto
-0.02 0 lineto
-0.04 0.01 lineto stroke
} ifelse
grestore
} def
% End of user PostScript
0 g
1.5 Mabswid
[ ] 0 setdash
.02381 .06816 m
.96176 .06816 L
s
.02381 .06816 m
.97619 .06816 L
s
% Start of user PostScript
-0.1 0 1.22 0 MAarrowhead1
% End of user PostScript
.9 Mabswid
.31241 .08449 m
.31241 .05184 L
s
.38456 .08449 m
.38456 .05184 L
s
.45671 .08449 m
.45671 .05184 L
s
.52886 .08449 m
.52886 .05184 L
s
.60101 .08449 m
.60101 .05184 L
s
.74531 .08449 m
.74531 .05184 L
s
.09596 .08449 m
.09596 .05184 L
s
.38456 .08449 m
.38456 .05184 L
s
.09596 .08449 m
.09596 .05184 L
s
.77417 .08449 m
.77417 .05184 L
s
.81746 .08449 m
.81746 .05184 L
s
gsave
.09596 .01918 -66 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(0) show
69.000 15.813 moveto
%%IncludeResource: font Times
%%IncludeFont: Times
/Times findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
gsave
.77417 .01918 -66 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(a) show
69.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
gsave
.81746 .01918 -66 -11.8438 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(n) show
69.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  ImageSize->{366.25, 43.8125},
  ImageMargins->{{44.25, 0}, {0, 0.625}},
  ImageRegion->{{0, 1}, {0, 1}},
  FontFamily->"Times New Roman",
  ImageCache->GraphicsData["Bitmap", "\<\
CF5dJ6E]HGAYHf4PAg9QL6QYHg<PAVmbKF5d0`40005^0000:a000`40O003h00OogooKgoo003oOom_
Ool00?moofmoo`00ogooKgoo000TOol3003^Ool200000goo0000000:Ool00`00Oomoo`020015Ool0
02=oo`05001oogooOol0003]Ool01000Ool000002goo00@007ooOol004Ioo`008goo00D007ooOomo
o`000>eoo`04001oogoo000<Ool01000Oomoo`00AGoo000SOol01@00Oomoogoo0000kGoo00D007oo
Oomoo`0000]oo`04001oogoo0015Ool002=oo`05001oogooOol0003^Ool01000Oomoo`002goo0P00
00=oo`00Ool0A7oo000SOol01@00Oomoogoo0000kgoo0`002Woo0P0000=oo`000000AGoo000SOol0
1@00Oomoogoo0000ogooAgoo000SOol01@00Oomoogoo0000ogooAgoo000TOol3003oOom8Ool00?mo
ofmoo`00ogooKgoo003oOom_Ool00?moofmoo`00ogooKgoo000VOol00`00Oomoo`1:Ool00`00Oomo
o`0GOol00`00Oomoo`0GOol00`00Oomoo`0FOol00`00Oomoo`0GOol00`00Oomoo`0aOol00`00Oomo
o`07Ool00`00Oomoo`0<Ool00`00Oomoo`14Ool002Ioo`03001oogoo04Yoo`03001oogoo01Moo`03
001oogoo01Moo`03001oogoo01Ioo`03001oogoo01Moo`03001oogoo035oo`03001oogoo00Moo`03
001oogoo00aoo`03001oogoo04Aoo`009Woo00<007ooOol0BWoo00<007ooOol05goo00<007ooOol0
5goo00<007ooOol05Woo00<007ooOol05goo00<007ooOol0<Goo00<007ooOol01goo00<007ooOol0
37oo00<007ooOol0:7oo0P006Woo000VOol00`00Oomoo`1:Ool00`00Oomoo`0GOol00`00Oomoo`0G
Ool00`00Oomoo`0FOol00`00Oomoo`0GOol00`00Oomoo`0aOol00`00Oomoo`07Ool00`00Oomoo`0<
Ool00`00Oomoo`0YOol5000FOol002Ioo`03001oogoo04Yoo`03001oogoo01Moo`03001oogoo01Mo
o`03001oogoo01Ioo`03001oogoo01Moo`03001oogoo035oo`03001oogoo00Moo`03001oogoo00ao
o`03001oogoo02]oo`H001=oo`009Woo00<007ooOol0BWoo00<007ooOol05goo00<007ooOol05goo
00<007ooOol05Woo00<007ooOol05goo00<007ooOol0<Goo00<007ooOol01goo00<007ooOol037oo
00<007ooOol0;Goo20003goo000<Oooo001F000=Ool002Ioo`03001oogoo04Yoo`03001oogoo01Mo
o`03001oogoo01Moo`03001oogoo01Ioo`03001oogoo01Moo`03001oogoo035oo`03001oogoo00Mo
o`03001oogoo00aoo`03001oogoo02eoo`P000moo`009Woo00<007ooOol0BWoo00<007ooOol05goo
00<007ooOol05goo00<007ooOol05Woo00<007ooOol05goo00<007ooOol0<Goo00<007ooOol01goo
00<007ooOol037oo00<007ooOol0:goo1P004goo000VOol00`00Oomoo`1:Ool00`00Oomoo`0GOol0
0`00Oomoo`0GOol00`00Oomoo`0FOol00`00Oomoo`0GOol00`00Oomoo`0aOol00`00Oomoo`07Ool0
0`00Oomoo`0<Ool00`00Oomoo`0YOol5000FOol002Ioo`03001oogoo04Yoo`03001oogoo01Moo`03
001oogoo01Moo`03001oogoo01Ioo`03001oogoo01Moo`03001oogoo035oo`03001oogoo00Moo`03
001oogoo00aoo`03001oogoo02Qoo`8001Yoo`009Woo00<007ooOol0BWoo00<007ooOol05goo00<0
07ooOol05goo00<007ooOol05Woo00<007ooOol05goo00<007ooOol0<Goo00<007ooOol01goo00<0
07ooOol037oo00<007ooOol0A7oo000VOol00`00Oomoo`1:Ool00`00Oomoo`0GOol00`00Oomoo`0G
Ool00`00Oomoo`0FOol00`00Oomoo`0GOol00`00Oomoo`0aOol00`00Oomoo`07Ool00`00Oomoo`0<
Ool00`00Oomoo`14Ool00?moofmoo`00ogooKgoo003oOom_Ool00?moofmoo`00ogooKgoo003oOom_
Ool00?moofmoo`00ogooKgoo003oOom_Ool00?moofmoo`00ogooKgoo003oOom_Ool00001\
\>"],
  ImageRangeCache->{{{91.625, 383.625}, {572.938, 538.938}} -> {-0.602417, \
56.1658, 0.00391345, 0.0864713}}],

Cell[TextData[{
  "Statt  ",
  StyleBox["a",
    FontSlant->"Italic"],
  "  liegt rechts von Null, wird die Schreibweise  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " > 0  gebraucht; gelesen  ",
  StyleBox["a",
    FontSlant->"Italic"],
  "  ist gr\[ODoubleDot]\[SZ]er Null, bzw.  ",
  StyleBox["a",
    FontSlant->"Italic"],
  "  ist positiv."
}], "Text",
  FontFamily->"Times New Roman"],

Cell[TextData[{
  StyleBox["\n",
    FontWeight->"Bold"],
  StyleBox["Anordnungsaxiome der reellen  Zahlen",
    FontFamily->"Arial",
    FontSize->12,
    FontWeight->"Bold"]
}], "Text",
  FontFamily->"Times New Roman",
  FontSize->14],

Cell["\<\
Die eben geschilderten anschaulichen Vorstellungen werden in den folgenden \
Axiomen \[UDoubleDot]ber die Anordnung von reellen Zahlen zusammen gefasst:\
\>", "Text",
  FontFamily->"Times New Roman"],

Cell[TextData[{
  StyleBox["A 1",
    FontWeight->"Bold"],
  "\tF\[UDoubleDot]r jede reelle Zahl  ",
  StyleBox["a",
    FontSlant->"Italic"],
  "  gilt genau eine der drei Beziehungen:\n\t\t",
  Cell[BoxData[
      \(TraditionalForm\`a > 0\)]],
  ", ",
  Cell[BoxData[
      \(TraditionalForm\`a = 0\)]],
  ", ",
  Cell[BoxData[
      \(TraditionalForm\`\(-a\) > 0\)]],
  " .\n\t\n",
  StyleBox["A 2",
    FontWeight->"Bold"],
  "\tSind  ",
  Cell[BoxData[
      \(TraditionalForm\`a, b > 0\)]],
  " , so gilt auch  ",
  Cell[BoxData[
      \(TraditionalForm\`a + b > 0\)]],
  "  und   ",
  Cell[BoxData[
      \(TraditionalForm\`\(\(a\[CenterDot]b\)\(>\)\(0\)\(\ \)\)\)]],
  ".\n\n",
  StyleBox["A 3",
    FontWeight->"Bold"],
  "\tDas Archimedisches Axiom:\n\tZu jedem  ",
  Cell[BoxData[
      \(TraditionalForm\`a \[Element] \ \[DoubleStruckCapitalR]\)]],
  "  gibt es ein  ",
  Cell[BoxData[
      \(TraditionalForm\`n \[Element] \[DoubleStruckCapitalN]\)]],
  "  mit  ",
  Cell[BoxData[
      \(TraditionalForm\`n - a > 0\)]],
  " .\n\nIn A 1 \[Dash] A 3 wird nur die Relation \"gr\[ODoubleDot]\[SZ]er \
als Null\" benutzt. Das ist insbesondere bei A 3 etwas \
umst\[ADoubleDot]ndlich.\n\nDie Menge der positiven reellen Zahlen, also der \
Zahlen gr\[ODoubleDot]\[SZ]er als Null, wird h\[ADoubleDot]ufig mit  ",
  Cell[BoxData[
      \(TraditionalForm\`\(\[DoubleStruckCapitalR]\^+\)\)]],
  " bezeichnet. Falls  \[Dash]",
  StyleBox["a",
    FontSlant->"Italic"],
  "  positiv ist, dann hei\[SZ]t  ",
  StyleBox["a",
    FontSlant->"Italic"],
  "  negativ.\n\nNeben der Eigenschaft positiv zu sein werden auch die Gr\
\[ODoubleDot]\[SZ]er-Relation  \">\", die Kleiner-Relation  \"<\", die Gr\
\[ODoubleDot]\[SZ]er-Gleich-Relation  \"\[GreaterEqual]\"  und die \
Kleiner-Gleich-Relation  \"\[LessEqual]\"  benutzt, die jetzt definiert \
werden.\n\n(",
  StyleBox["i",
    FontSlant->"Italic"],
  ")\t",
  StyleBox["a > b  ,  ",
    FontSlant->"Italic"],
  "falls\t",
  StyleBox["a",
    FontSlant->"Italic"],
  " \[Dash] ",
  StyleBox["b",
    FontSlant->"Italic"],
  " > 0 ,\t\t \t",
  StyleBox["a",
    FontSlant->"Italic"],
  "  ist gr\[ODoubleDot]\[SZ]er als  ",
  StyleBox["b ,",
    FontSlant->"Italic"],
  "\n(",
  StyleBox["ii",
    FontSlant->"Italic"],
  ")\t",
  StyleBox["b < a  ,",
    FontSlant->"Italic"],
  "\t falls\t",
  StyleBox["a",
    FontSlant->"Italic"],
  " >",
  StyleBox[" b ,",
    FontSlant->"Italic"],
  "\t\t\t\t",
  StyleBox["b",
    FontSlant->"Italic"],
  "  ist kleiner als  ",
  StyleBox["a , ",
    FontSlant->"Italic"],
  "\n(",
  StyleBox["iii",
    FontSlant->"Italic"],
  ")\t",
  StyleBox["a",
    FontSlant->"Italic"],
  " \[GreaterEqual]",
  StyleBox[" b  ,",
    FontSlant->"Italic"],
  "\t falls\t",
  StyleBox["a > b",
    FontSlant->"Italic"],
  "  oder  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " = ",
  StyleBox["b ,\t\t    a",
    FontSlant->"Italic"],
  "  ist gr\[ODoubleDot]\[SZ]er oder gleich  ",
  StyleBox["b ,",
    FontSlant->"Italic"],
  "\n(",
  StyleBox["iv",
    FontSlant->"Italic"],
  ")\t",
  StyleBox["a",
    FontSlant->"Italic"],
  " \[LessEqual]",
  StyleBox[" b  ,",
    FontSlant->"Italic"],
  "\t falls\t",
  StyleBox["a",
    FontSlant->"Italic"],
  " < ",
  StyleBox["b",
    FontSlant->"Italic"],
  "  oder  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " = ",
  StyleBox["b ,",
    FontSlant->"Italic"],
  "\t \t ",
  StyleBox["a",
    FontSlant->"Italic"],
  "  ist kleiner oder gleich  ",
  StyleBox["b .\n\n",
    FontSlant->"Italic"],
  "Bemerkung: \"Falls\" wird hier in der Bedeutung von \"genau dann wenn\" \
benutzt!",
  StyleBox["\n\n",
    FontSlant->"Italic"],
  "Aus den Axiomen A 1 und A 2 folgen \n\n",
  StyleBox["Regeln f\[UDoubleDot]r das Rechnen mit Ungleichungen: ",
    FontFamily->"Arial",
    FontWeight->"Bold"],
  "\n\nEs seien  ",
  Cell[BoxData[
      \(TraditionalForm\`a, b, 
      c, \[Alpha], \[Beta]\  \[Element] \ \[DoubleStruckCapitalR]\)]],
  " .\n\n1.\tAus  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " > ",
  StyleBox["b",
    FontSlant->"Italic"],
  "  und  ",
  StyleBox["b",
    FontSlant->"Italic"],
  " > ",
  StyleBox["c",
    FontSlant->"Italic"],
  "  folgt  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " > ",
  StyleBox["c",
    FontSlant->"Italic"],
  " ,  also die Transitivit\[ADoubleDot]t von \" > \".\n2.\tAus  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " > ",
  StyleBox["b",
    FontSlant->"Italic"],
  "  folgen\n2.1\t",
  StyleBox["a",
    FontSlant->"Italic"],
  " + ",
  StyleBox["c",
    FontSlant->"Italic"],
  " > ",
  StyleBox["b",
    FontSlant->"Italic"],
  " + ",
  StyleBox["c ,\t   ",
    FontSlant->"Italic"],
  "f\[UDoubleDot]r alle  ",
  Cell[BoxData[
      \(TraditionalForm\`c \[Element] \[DoubleStruckCapitalR]\)]],
  ",\n2.2\t",
  StyleBox["a",
    FontSlant->"Italic"],
  " \[CenterDot] c > ",
  StyleBox["b",
    FontSlant->"Italic"],
  " \[CenterDot] ",
  StyleBox["c ,\t\t   ",
    FontSlant->"Italic"],
  "f\[UDoubleDot]r  ",
  StyleBox["c",
    FontSlant->"Italic"],
  " >",
  StyleBox[" ",
    FontSlant->"Italic"],
  "0 ,",
  StyleBox["\n",
    FontSlant->"Italic"],
  "2.3\t",
  StyleBox["a",
    FontSlant->"Italic"],
  " \[CenterDot] ",
  StyleBox["c",
    FontSlant->"Italic"],
  " < ",
  StyleBox["b",
    FontSlant->"Italic"],
  " \[CenterDot] ",
  StyleBox["c ,\t\t   ",
    FontSlant->"Italic"],
  "f\[UDoubleDot]r  ",
  StyleBox["c",
    FontSlant->"Italic"],
  " < 0 ,\n2.4\t",
  Cell[BoxData[
      FormBox[
        StyleBox[\(1\/a\),
          FontSize->14], TraditionalForm]]],
  "<",
  Cell[BoxData[
      FormBox[
        StyleBox[\(1\/b\),
          FontSize->14], TraditionalForm]]],
  ",\t\t f\[UDoubleDot]r  ",
  StyleBox["b",
    FontSlant->"Italic"],
  " >",
  StyleBox[" ",
    FontSlant->"Italic"],
  "0",
  StyleBox[" .",
    FontSlant->"Italic"]
}], "Text",
  FontFamily->"Times New Roman"],

Cell[TextData[{
  StyleBox["Beweis zu 1:",
    FontFamily->"Arial"],
  "\nNach (",
  StyleBox["i",
    FontSlant->"Italic"],
  ") folgt aus  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " > ",
  StyleBox["b",
    FontSlant->"Italic"],
  "  und  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " > ",
  StyleBox["c",
    FontSlant->"Italic"],
  "  direkt  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " \[Dash] ",
  StyleBox["b",
    FontSlant->"Italic"],
  " > 0  und  ",
  StyleBox["b",
    FontSlant->"Italic"],
  " \[Dash] ",
  StyleBox["c",
    FontSlant->"Italic"],
  " > 0, also nach A 2 ",
  Cell[BoxData[
      \(TraditionalForm\`a + c = \((a - b)\) + \((b - c)\) > 0\)]],
  " , \nd.h.  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " > ",
  StyleBox["c",
    FontSlant->"Italic"],
  "  nach (",
  StyleBox["i",
    FontSlant->"Italic"],
  ") .\n\n",
  StyleBox["Beweis zu 2.1:",
    FontFamily->"Arial"],
  "\n",
  StyleBox["a",
    FontSlant->"Italic"],
  " >",
  StyleBox[" b",
    FontSlant->"Italic"],
  "  bedeutet nach (",
  StyleBox["i",
    FontSlant->"Italic"],
  ")  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " \[Dash] ",
  StyleBox["b",
    FontSlant->"Italic"],
  " > 0, also ist auch  ",
  Cell[BoxData[
      \(TraditionalForm\`\((a + c)\) - \((b + c)\) > 0\)]],
  " , was nach (",
  StyleBox["i",
    FontSlant->"Italic"],
  ")  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " + ",
  StyleBox["c",
    FontSlant->"Italic"],
  " > ",
  StyleBox["b",
    FontSlant->"Italic"],
  " +",
  StyleBox[" c",
    FontSlant->"Italic"],
  "  ergibt.\n\n",
  StyleBox["Beweis zu 2.2:",
    FontFamily->"Arial"],
  "\nMit A 2 folgt aus  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " \[Dash]",
  StyleBox[" b",
    FontSlant->"Italic"],
  " > 0  f\[UDoubleDot]r  ",
  StyleBox["c",
    FontSlant->"Italic"],
  " >",
  StyleBox[" ",
    FontSlant->"Italic"],
  "0  auch  ",
  Cell[BoxData[
      \(TraditionalForm\`\((a - b)\)\[CenterDot]c > 0\)]],
  " , d.h.  ",
  StyleBox["a",
    FontSlant->"Italic"],
  "\[CenterDot]",
  StyleBox["c",
    FontSlant->"Italic"],
  " \[Dash]  ",
  StyleBox["b",
    FontSlant->"Italic"],
  "\[CenterDot]",
  StyleBox["c",
    FontSlant->"Italic"],
  " > 0 ,  also ",
  StyleBox[" a\[CenterDot]c",
    FontSlant->"Italic"],
  " > ",
  StyleBox["b\[CenterDot]c",
    FontSlant->"Italic"],
  " nach (",
  StyleBox["i",
    FontSlant->"Italic"],
  ").\nBeweis zu 2.3 analog.\n\n",
  StyleBox["Beweis zu 2.4:",
    FontFamily->"Arial"],
  "\nNach A 2 ist mit  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " > ",
  StyleBox["b",
    FontSlant->"Italic"],
  " >",
  StyleBox[" ",
    FontSlant->"Italic"],
  "0  auch  ",
  StyleBox["a\[CenterDot]b",
    FontSlant->"Italic"],
  " > 0 .\nW\[ADoubleDot]re nun zuerst ",
  Cell[BoxData[
      FormBox[
        StyleBox[\(1\/a\),
          FontSize->14], TraditionalForm]]],
  ">",
  Cell[BoxData[
      FormBox[
        StyleBox[\(1\/b\),
          FontSize->14], TraditionalForm]]],
  ", so w\[UDoubleDot]rde mit 2.2 durch Multiplikation mit  ",
  StyleBox["a",
    FontSlant->"Italic"],
  "\[CenterDot]",
  StyleBox["b",
    FontSlant->"Italic"],
  "  folgen  ",
  Cell[BoxData[
      FormBox[
        RowBox[{"b", "=", 
          RowBox[{
            RowBox[{
              StyleBox[\(\(a\[CenterDot]b\)\/a\),
                FontSize->14], ">", 
              StyleBox[\(\(a\[CenterDot]b\)\/b\),
                FontSize->14]}], "=", "a"}]}], TraditionalForm]]],
  " . \nDas ist ein Widerspruch. \nZweitens folgt aber aus ",
  Cell[BoxData[
      FormBox[
        StyleBox[\(1\/a\),
          FontSize->14], TraditionalForm]]],
  "=",
  Cell[BoxData[
      FormBox[
        StyleBox[\(1\/b\),
          FontSize->14], TraditionalForm]]],
  " auch  ",
  Cell[BoxData[
      \(TraditionalForm\`a = b\)]],
  " , also ebenfalls ein Widerspruch.\n\n3.\tAus \t",
  StyleBox["a",
    FontSlant->"Italic"],
  " > ",
  StyleBox["b",
    FontSlant->"Italic"],
  "  und   ",
  Cell[BoxData[
      \(TraditionalForm\`\[Alpha] > \[Beta]\)]],
  " folgen:\n3.1\t\t",
  Cell[BoxData[
      \(TraditionalForm\`a + \[Alpha] > b + \[Beta]\)]],
  " ,\n3.2\t\t",
  Cell[BoxData[
      \(TraditionalForm\`a\[CenterDot]\[Alpha] > b\[CenterDot]\[Beta]\)]],
  " ,  falls  ",
  Cell[BoxData[
      \(TraditionalForm\`b, \[Beta] > 0\)]],
  " . \n\n",
  StyleBox["Beweis f\[UDoubleDot]r 3.1:",
    FontFamily->"Arial"],
  "\nAus  ",
  Cell[BoxData[
      \(TraditionalForm\`a > b\)]],
  StyleBox["  ",
    FontSlant->"Italic"],
  "folgt mit 2.1 ",
  Cell[BoxData[
      \(TraditionalForm\`a + \[Alpha] > b + \[Alpha]\)]],
  " . Aus  ",
  Cell[BoxData[
      \(TraditionalForm\`\[Alpha] > \[Beta]\)]],
  " folgt mit 2.1 ",
  Cell[BoxData[
      \(TraditionalForm\`\[Alpha] + b > \[Beta] + b\)]],
  " .\nMit der Transitivit\[ADoubleDot]t von  \">\"  folgt  ",
  Cell[BoxData[
      \(TraditionalForm\`a + \[Alpha] > 
          b + \[Alpha] = \ \(\[Alpha] + b > \[Beta] + b = b + \[Beta]\)\)]],
  " .",
  StyleBox[" ",
    FontSlant->"Italic"],
  "\nDer ",
  StyleBox["Beweis f\[UDoubleDot]r 3.2",
    FontFamily->"Arial"],
  " verl\[ADoubleDot]uft analog.\n\n4.\tF\[UDoubleDot]r  ",
  Cell[BoxData[
      \(TraditionalForm\`a \[NotEqual] 0\)]],
  "  gilt  ",
  Cell[BoxData[
      \(TraditionalForm\`a\^2 > 0\)]],
  " .\n\n",
  StyleBox["Beweis: ",
    FontFamily->"Arial"],
  "\nIst  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " > 0 , so folgt  ",
  Cell[BoxData[
      \(TraditionalForm\`a\^2 > 0\)]],
  "  mit  A 2. Ist  \[Dash]",
  StyleBox["a",
    FontSlant->"Italic"],
  " > 0 ,  so folgt  ",
  Cell[BoxData[
      \(TraditionalForm\`a\^2 = \((\(-a\)\ )\)\[CenterDot]\((\(-a\))\) > 
          0\)]],
  " analog.\n\n4.1\tAus 4. folgt  1 = 1 \[CenterDot] 1 > 0 ,  da  1 \
\[NotEqual] 0  und mit A 2 dann auch  \[Dash]1 < 0 .\n\n4.2\tF\[UDoubleDot]r  \
",
  StyleBox["a",
    FontSlant->"Italic"],
  " > 0  gilt  ",
  Cell[BoxData[
      FormBox[
        RowBox[{
          StyleBox[\(1\/a\),
            FontSize->14], ">", "0"}], TraditionalForm]]],
  " .\n\n",
  StyleBox["Beweis:",
    FontFamily->"Arial"],
  " \nNach 4. ist  ",
  Cell[BoxData[
      \(TraditionalForm\`a\^2 > 0\)]],
  " . W\[ADoubleDot]re  ",
  Cell[BoxData[
      FormBox[
        RowBox[{
          StyleBox[\(1\/a\),
            FontSize->14], 
          StyleBox["=",
            FontSize->14], "0"}], TraditionalForm]]],
  " ,  so w\[ADoubleDot]re auch  ",
  Cell[BoxData[
      FormBox[
        RowBox[{"a", "=", " ", 
          RowBox[{
            RowBox[{\(a\^2\), "\[CenterDot]", 
              StyleBox[\(1\/a\),
                FontSize->14]}], "=", "0"}]}], TraditionalForm]]],
  "  im Widerspruch zur Voraussetzung  ",
  StyleBox["a",
    FontSlant->"Italic"],
  " > 0 .\nW\[ADoubleDot]re 0 > ",
  Cell[BoxData[
      FormBox[
        StyleBox[\(1\/a\),
          FontSize->14], TraditionalForm]]],
  " , so w\[UDoubleDot]rde mit 2.2   ",
  Cell[BoxData[
      FormBox[
        RowBox[{
          RowBox[{"0", ">", 
            RowBox[{
              StyleBox[\(1\/a\),
                FontSize->14], "\[CenterDot]", \(a\^2\)}]}], "=", "a"}], 
        TraditionalForm]]],
  " gelten, ebenfalls ein Widerspruch. Also bleibt nach A 1 nur  ",
  Cell[BoxData[
      FormBox[
        RowBox[{
          StyleBox[\(1\/a\),
            FontSize->14], ">", "0"}], TraditionalForm]]],
  " \[UDoubleDot]brig."
}], "Text",
  FontFamily->"Times New Roman"],

Cell[TextData[{
  "5.\tEs seien   ",
  Cell[BoxData[
      \(TraditionalForm\`a, b, x \[Element] \ \[DoubleStruckCapitalR]\)]],
  "  mit  ",
  Cell[BoxData[
      \(TraditionalForm\`b, x > 0\)]],
  ".\n\n\tDann gilt  ",
  Cell[BoxData[
      FormBox[
        StyleBox[\(\(a\  - \ x\)\/b\),
          FontSize->16], TraditionalForm]]],
  "<",
  Cell[BoxData[
      FormBox[
        StyleBox[\(a\/b\),
          FontSize->16], TraditionalForm]],
    FontSize->14],
  "<",
  Cell[BoxData[
      FormBox[
        StyleBox[\(\(a\  + \ x\)\/b\),
          FontSize->16], TraditionalForm]],
    FontSize->14],
  " ."
}], "Text",
  FontFamily->"Times New Roman"],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: 1.4 
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% Graphics
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12  scalefont  setfont
% Scaling calculations
0.0238095 0.380952 0.433333 0.533333 [
[.40476 .42083 -5 -15.6875 ]
[.40476 .42083 5 0 ]
[.78571 .42083 -5 -15.6875 ]
[.78571 .42083 5 0 ]
[.01131 .7 -16.1875 -12.0625 ]
[.01131 .7 0 12.0625 ]
[ 0 0 0 0 ]
[ 1 1.4 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.40476 .43333 m
.40476 .43958 L
s
gsave
.40476 .42083 -66 -19.6875 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(a) show
69.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
.78571 .43333 m
.78571 .43958 L
s
gsave
.78571 .42083 -66 -19.6875 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(b) show
69.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
0 .43333 m
1 .43333 L
s
.02381 .7 m
.03006 .7 L
s
gsave
.01131 .7 -77.1875 -16.0625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 32.125 translate 1 -1 scale
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding WindowsANSIEncoding def
        currentdict
    end

    newfontname exch definefont pop
} def
63.000 18.625 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
%%BeginResource: font Times-Italic-MISO
%%BeginFont: Times-Italic-MISO
/Times-Italic /Times-Italic-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
66.063 10.375 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(a) show
%%IncludeResource: font Math1
%%IncludeFont: Math1
/Math1 findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
64.750 18.625 moveto
(\\200\\200) show
68.250 18.625 moveto
(\\200\\200) show
71.438 18.625 moveto
(\\200) show
66.063 27.063 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(b) show
75.188 18.625 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
.02381 0 m
.02381 1.4 L
s
0 0 m
1 0 L
1 1.4 L
0 1.4 L
closepath
clip
newpath
0 0 1 r
1.5 Mabswid
.02381 .7 m
.06244 .67296 L
.10458 .64346 L
.14415 .61576 L
.18221 .58912 L
.22272 .56076 L
.26171 .53347 L
.30316 .50446 L
.34309 .47651 L
.3815 .44962 L
.42237 .42101 L
.46172 .39347 L
.49955 .36698 L
.53984 .33878 L
.57861 .31164 L
.61984 .28278 L
.65954 .25499 L
.69774 .22825 L
.73838 .1998 L
.77751 .17241 L
.81909 .1433 L
.85916 .11525 L
.89771 .08827 L
.93871 .05957 L
.97619 .03333 L
s
0 0 0 r
.02381 .7 m
.06244 .7 L
.10458 .7 L
.14415 .7 L
.18221 .7 L
.22272 .7 L
.26171 .7 L
.30316 .7 L
.34309 .7 L
.3815 .7 L
.42237 .7 L
.46172 .7 L
.49955 .7 L
.53984 .7 L
.57861 .7 L
.61984 .7 L
.65954 .7 L
.69774 .7 L
.73838 .7 L
.77751 .7 L
.81909 .7 L
.85916 .7 L
.89771 .7 L
.93871 .7 L
.97619 .7 L
s
1 0 0 r
.02381 .7 m
.06244 .72704 L
.10458 .75654 L
.14415 .78424 L
.18221 .81088 L
.22272 .83924 L
.26171 .86653 L
.30316 .89554 L
.34309 .92349 L
.3815 .95038 L
.42237 .97899 L
.46172 1.00653 L
.49955 1.03302 L
.53984 1.06122 L
.57861 1.08836 L
.61984 1.11722 L
.65954 1.14501 L
.69774 1.17175 L
.73838 1.2002 L
.77751 1.22759 L
.81909 1.2567 L
.85916 1.28475 L
.89771 1.31173 L
.93871 1.34043 L
.97619 1.36667 L
s
gsave
.88095 1.18 -78.0938 -16.5 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 33 translate 1 -1 scale
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding WindowsANSIEncoding def
        currentdict
    end

    newfontname exch definefont pop
} def
63.000 19.500 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
%%BeginResource: font Times-Italic-MISO
%%BeginFont: Times-Italic-MISO
/Times-Italic /Times-Italic-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
66.063 11.250 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
(a) show
74.438 11.250 moveto
%%IncludeResource: font Math1
%%IncludeFont: Math1
/Math1 findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
(+) show
84.813 11.250 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
(x) show
%%IncludeResource: font Math1
%%IncludeFont: Math1
/Math1 findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
64.750 19.500 moveto
(\\200\\200\\200\\200\\200\\200\\200\\200) show
78.750 19.500 moveto
(\\200\\200\\200\\200) show
85.750 19.500 moveto
(\\200\\200) show
89.438 19.500 moveto
(\\200) show
75.063 27.938 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
(b) show
93.188 19.500 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
0 0 1 r
gsave
.88095 .22 -78.0938 -16.0625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 32.125 translate 1 -1 scale
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding WindowsANSIEncoding def
        currentdict
    end

    newfontname exch definefont pop
} def
63.000 18.625 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
%%BeginResource: font Times-Italic-MISO
%%BeginFont: Times-Italic-MISO
/Times-Italic /Times-Italic-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
0.000 0.000 rmoveto
66.063 10.375 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
(a) show
74.438 10.375 moveto
%%IncludeResource: font Math1
%%IncludeFont: Math1
/Math1 findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
(-) show
84.813 10.375 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
(x) show
%%IncludeResource: font Math1
%%IncludeFont: Math1
/Math1 findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
64.750 18.625 moveto
(\\200\\200\\200\\200\\200\\200\\200\\200) show
78.750 18.625 moveto
(\\200\\200\\200\\200) show
85.750 18.625 moveto
(\\200\\200) show
89.438 18.625 moveto
(\\200) show
75.063 27.063 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
(b) show
93.188 18.625 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  ImageSize->{174.438, 244.063},
  ImageMargins->{{108.313, 0}, {0, 0}},
  ImageRegion->{{0, 1}, {0, 1}},
  ImageCache->GraphicsData["Bitmap", "\<\
CF5dJ6E]HGAYHf4PAg9QL6QYHg<PAVmbKF5d0`40002^0000m1000`40O003h00O[Woo002^Ool00:io
o`00[Woo002^Ool00:ioo`00[Woo002^Ool00:ioo`00[Woo002^Ool0019oo`03001oogoo09Uoo`00
4Woo00<007ooOol0VGoo000BOol00`00Oomoo`2IOol0019oo`03001oogoo09Uoo`004Woo00<007oo
Ool0VGoo000BOol00`00Oomoo`2DOol00`0OOomoo`02Ool0019oo`03001oogoo099oo`807`Eoo`00
4Woo00<007ooOol0TGoo00<07gooOol01Goo000BOol00`00Oomoo`2?Ool201l8Ool0019oo`03001o
ogoo08ioo`0301moogoo00Qoo`004Woo00<007ooOol0SGoo00<07gooOol02Goo000BOol00`00Oomo
o`2<Ool00`0OOomoo`0:Ool0019oo`03001oogoo08Yoo`807`eoo`004Woo00<007ooOol0RGoo00<0
7gooOol03Goo000BOol00`00Oomoo`28Ool00`0OOomoo`0>Ool0019oo`03001oogoo08Ioo`807a5o
o`004Woo00<007ooOol0QGoo00<07gooOol04Goo000BOol00`00Oomoo`23Ool201lDOol0019oo`03
001oogoo089oo`0301moogoo01Aoo`004Woo00<007ooOol0P7oo0P0O5goo000BOol00`00Oomoo`1n
Ool201lIOol0019oo`03001oogoo07aoo`807a]oo`004Woo00<007ooOol0Ngoo00<07gooOol06goo
000BOol00`00Oomoo`1jOol00`0OOomoo`0LOol0019oo`03001oogoo07Uoo`0301moogoo01eoo`00
4Woo00<007ooOol0Mgoo0P0O2Woo0P0O57oo000BOol00`00Oomoo`1fOol00`0OOomoo`09Ool0100O
Oomoo`0O4goo000BOol00`00Oomoo`1eOol00`0OOomoo`0:Ool01@0OOomoogoo01l04Woo000BOol0
0`00Oomoo`1cOol201l>Ool0100OOomoo`0O4Woo000BOol00`00Oomoo`1aOol201l@Ool201l00goo
01moo`0AOol0019oo`03001oogoo06moo`807a9oo`0401moo`0O01lBOol0019oo`03001oogoo06io
o`0301moogoo019oo`0301moogoo01=oo`004Woo00<007ooOol0KGoo00<07gooOol057oo00<07goo
Ool04Woo000BOol00`00Oomoo`1/Ool00`0OOomoo`0DOol201lDOol0019oo`03001oogoo06Yoo`80
7beoo`004Woo00<007ooOol0JGoo00<07gooOol0;Goo000BOol00`00Oomoo`1XOol00`0OOomoo`0=
OolJ01l7Ool0019oo`03001oogoo06Ioo`807c5oo`004Woo00<007ooOol0IGoo00<07gooOol0<Goo
000BOol00`00Oomoo`1SOol201ldOol0019oo`03001oogoo069oo`0301moogoo03Aoo`004Woo00<0
07ooOol0H7oo0P0O5goo0P0O00=oo`0O01l03Woo00@07gooOol07`Uoo`004Woo00<007ooOol0Ggoo
00<07gooOol05goo00@07goo01l07a1oo`0301moo`0O00Uoo`004Woo00<007ooOol0GWoo00<07goo
Ool067oo00@07gooOol07a5oo`0301moogoo00Qoo`004Woo00<007ooOol0G7oo0P0O6goo00D07goo
Oomoo`0O00Aoo`L07`Eoo`0301moogoo00Qoo`004Woo00<007ooOol0Fgoo00<07gooOol077oo00@0
7gooOol07a1oo`807`Uoo`004Woo00<007ooOol0FGoo0P0O87oo0`0O3goo0P0O00=oo`0OOol01goo
000BOol00`00Oomoo`1HOol00`0OOomoo`0nOol0019oo`03001oogoo05Ioo`807d5oo`004Woo00<0
07ooOol0EGoo00<07gooOol0@Goo000BOol00`00Oomoo`1DOol00`0OOomoo`12Ool0019oo`03001o
ogoo05=oo`0301moogoo04=oo`004Woo00<007ooOol0DGoo0P0OAWoo000BOol00`00Oomoo`1@Ool0
0`0OOomoo`16Ool0019oo`03001oogoo04moo`0301moogoo04Moo`004Woo00<007ooOol0CGoo0P0O
BWoo000BOol00`00Oomoo`0fOol200000goo0000000@Ool201lWOol2000SOol0019oo`03001oogoo
03Ioo`04001oo`00000?Ool201lXOol01000Oomoo`008Woo000BOol00`00Oomoo`0fOol01000Oomo
o`003Woo00<07gooOol0:7oo00D007ooOomoo`00025oo`004Woo00<007ooOol0=Woo00D007ooOomo
o`0000]oo`807baoo`04001oogoo000QOol0019oo`03001oogoo03Moo`04001oogoo000:Ool00`0O
Oomoo`0/Ool200000goo001oo`0POol0019oo`03001oogoo03Qoo`<000Qoo`807bmoo`04001oo`00
000QOol0019oo`03001oogoo049oo`0301moogoo02moo`03001oogoo029oo`004Woo00<007ooOol0
@Goo00<07gooOol0<Goo00<007ooOol08Goo000BOol00`00Oomoo`10Ool00`0OOomoo`0aOol2000S
Ool0019oo`03001oogoo03ioo`807eUoo`004Woo00<007ooOol0?Goo00<07gooOol0FGoo000BOol0
0`00Oomoo`0lOol00`0OOomoo`1JOol0019oo`03001oogoo03Yoo`807eeoo`003Woo@00000<07`00
0000G@00000BOol00`00Oomoo`0gOol201l00`00Oomoo`0jOol00`00Oomoo`0POol0019oo`03001o
ogoo03Ioo`0301moogoo061oo`004Woo00<007ooOol0=7oo0P0OHgoo000BOol00`00Oomoo`0bOol2
01mUOol0019oo`03001oogoo031oo`807fMoo`004Woo00<007ooOol0;goo00<07gooOol0Igoo000B
Ool00`00Oomoo`0^Ool00`0OOomoo`1XOol0019oo`03001oogoo02eoo`0301moogoo06Uoo`004Woo
00<007ooOol0:goo0P0OK7oo000BOol00`00Oomoo`0ZOol00`0OOomoo`1/Ool0019oo`03001oogoo
02Uoo`0301moogoo06eoo`004Woo00<007ooOol09goo0P0OL7oo000BOol00`00Oomoo`0VOol00`0O
Oomoo`1`Ool0019oo`03001oogoo02Aoo`807g=oo`004Woo00<007ooOol08goo00<07gooOol0Lgoo
000BOol00`00Oomoo`0QOol201mfOol0019oo`03001oogoo021oo`0301moogoo07Ioo`004Woo00<0
07ooOol07goo00<07gooOol0Mgoo000BOol00`00Oomoo`0MOol201mjOol0019oo`03001oogoo01ao
o`0301moogoo07Yoo`004Woo00<007ooOol06Woo0P0OOGoo000BOol00`00Oomoo`0IOol00`0OOomo
o`1mOol0019oo`03001oogoo01Moo`807h1oo`004Woo00<007ooOol05Woo00<07gooOol0P7oo000B
Ool00`00Oomoo`0EOol00`0OOomoo`21Ool0019oo`03001oogoo01Aoo`0301moogoo089oo`004Woo
00<007ooOol04Woo0P0OQGoo000BOol00`00Oomoo`0AOol00`0OOomoo`25Ool0019oo`03001oogoo
011oo`0301moogoo08Ioo`004Woo00<007ooOol03Woo0P0ORGoo000BOol00`00Oomoo`0=Ool00`0O
Oomoo`29Ool000Ioo`8000Yoo`03001oogoo00]oo`807haoo`001Goo00@007ooOol000Uoo`03001o
ogoo00Yoo`0301moogoo08aoo`001Goo00D007ooOomoo`0000Qoo`03001oogoo00Qoo`807hmoo`00
1Woo00@007ooOol000Qoo`03001oogoo00Moo`0301moogoo08moo`001Woo0P0000=oo`00Ool01goo
00<007ooOol01Woo00<07gooOol0T7oo0006Ool01000Ool0000027oo00<007ooOol017oo0P0OTgoo
0006Ool00`00Oomoo`09Ool00`00Oomoo`03Ool00`0OOomoo`2COol000Moo`03001oogoo00Qoo`04
001oogooOol201nFOol000Ioo`8000Yoo`04001oogoo01nHOol0019oo`0300007`0O09Uoo`004Woo
00=l00000000U@0017oo0003Ool90006Ool00`00O01l002IOol0019oo`04001oogooO02HOol0019o
o`04001oogooOol2O02FOol0019oo`03001oogoo00=oo`03O01oogoo09=oo`004Woo00<007ooOol0
17oo0W`0Tgoo000BOol00`00Oomoo`06Ool00g`0Oomoo`2@Ool000Eoo`800003Ool0000000Qoo`03
001oogoo00Moo`03O01oogoo08moo`001Goo00@007oo000000Uoo`03001oogoo00Qoo`9l08moo`00
1Goo00@007ooOol000Uoo`03001oogoo00Yoo`03O01oogoo08aoo`001Goo00D007ooOomoo`0000Qo
o`03001oogoo00]oo`9l08aoo`001Woo00@007ooOol000Qoo`03001oogoo00eoo`03O01oogoo08Uo
o`001goo0`0027oo00<007ooOol03Woo0W`0RGoo000BOol00`00Oomoo`0@Ool00g`0Oomoo`26Ool0
019oo`03001oogoo015oo`03O01oogoo08Eoo`004Woo00<007ooOol04Woo00=l07ooOol0Q7oo000B
Ool00`00Oomoo`0COol2O024Ool0019oo`03001oogoo01Eoo`03O01oogoo085oo`004Woo00<007oo
Ool05Woo00=l07ooOol0P7oo000BOol00`00Oomoo`0GOol2O020Ool0019oo`03001oogoo01Uoo`03
O01oogoo07eoo`004Woo00<007ooOol06Woo0W`0OGoo000BOol00`00Oomoo`0LOol00g`0Oomoo`1j
Ool0019oo`03001oogoo01eoo`9l07Yoo`004Woo00<007ooOol07goo0W`0N7oo000BOol00`00Oomo
o`0QOol2O01fOol0019oo`03001oogoo02=oo`03O01oogoo07=oo`004Woo00<007ooOol097oo00=l
07ooOol0LWoo000BOol00`00Oomoo`0UOol00g`0Oomoo`1aOol0019oo`03001oogoo02Ioo`9l075o
o`004Woo00<007ooOol0:7oo00=l07ooOol0KWoo000BOol00`00Oomoo`0YOol00g`0Oomoo`1]Ool0
019oo`03001oogoo02Yoo`03O01oogoo06aoo`004Woo00<007ooOol0:goo00=l07ooOol0Jgoo000B
Ool00`00Oomoo`0/Ool2O01[Ool0019oo`03001oogoo02ioo`03O01oogoo06Qoo`004Woo00<007oo
Ool0;goo00=l07ooOol0Igoo000BOol00`00Oomoo`0`Ool2O01WOol0019oo`03001oogoo039oo`9l
06Eoo`004Woo00<007ooOol0=7oo0W`0Hgoo000BOol00`00Oomoo`0fOol00g`0Oomoo`1POol0019o
o`03001oogoo03Moo`9l061oo`004Woo00<007ooOol0>Goo00=l07ooOol0GGoo000BOol00`00Oomo
o`0jOol2O01MOol0019oo`03001oogoo03aoo`03O01oogoo05Yoo`004Woo00<007ooOol0?Goo00=l
07ooOol0FGoo000BOol00`00Oomoo`0nOol00g`0Oomoo`1HOol0019oo`03001oogoo03moo`9l05Qo
o`004Woo00<007ooOol0@Goo00=l07ooOol0EGoo000BOol00`00Oomoo`12Ool00g`0Oomoo`1DOol0
019oo`03001oogoo04=oo`9l05Aoo`004Woo00<007ooOol0AGoo00=l07ooOol0DGoo000BOol00`00
Oomoo`16Ool2O01AOol0019oo`03001oogoo04Qoo`03O01oogoo04ioo`004Woo00<007ooOol0BGoo
0W`0CWoo000BOol00`00Oomoo`1;Ool2O01<Ool0019oo`03001oogoo04eoo`9l04Yoo`004Woo00<0
07ooOol0Cgoo00=l07ooOol0Agoo000BOol00`00Oomoo`1@Ool00g`0Oomoo`16Ool0019oo`03001o
ogoo055oo`03O01oogoo04Eoo`004Woo00<007ooOol0DWoo0W`0AGoo000BOol00`00Oomoo`1DOol0
0g`0Oomoo`12Ool0019oo`03001oogoo05Eoo`03O01oogoo045oo`004Woo00<007ooOol0EWoo0W`0
@Goo000BOol00`00Oomoo`1HOol00g`0Oomoo`0nOol0019oo`03001oogoo05Uoo`9l03ioo`004Woo
00<007ooOol0Fgoo00=l07ooOol09Goo0W`057oo000BOol00`00Oomoo`1LOol2O00TOol017`0Oomo
og`04goo000BOol00`00Oomoo`1NOol00g`0Oomoo`0QOol01G`0OomoogooO0004Woo000BOol00`00
Oomoo`1OOol00g`0Oomoo`0QOol017`0Oomoog`04Woo000BOol00`00Oomoo`1POol2O00QOol2O000
0gooO01oo`0AOol0019oo`03001oogoo069oo`03O01oogoo01ioo`04O01oog`0O00BOol0019oo`03
001oogoo06=oo`9l01ioo`03O01oogoo01=oo`004Woo00<007ooOol0IGoo00=l07ooOol077oo00=l
07ooOol04Woo000BOol00`00Oomoo`1VOol2O00KOol2O00DOol0019oo`03001oogoo06Qoo`03O01o
ogoo02ioo`004Woo00<007ooOol0JGoo00=l07ooOol0;Goo000BOol00`00Oomoo`1ZOol00g`0Oomo
o`0;OolJO007Ool0019oo`03001oogoo06]oo`9l02aoo`004Woo00<007ooOol0KGoo00=l07ooOol0
:Goo000BOol00`00Oomoo`1^Ool00g`0Oomoo`0XOol0019oo`03001oogoo06moo`9l02Qoo`004Woo
00<007ooOol0LGoo0W`09Woo000BOol00`00Oomoo`1cOol2O004Ool2O0000gooO01l0007Ool00g`0
Oomoo`04Ool017`0Oomoog`02Goo000BOol00`00Oomoo`1eOol01W`0OomoogooO01oo`9l00Qoo`03
O01oogoo00Eoo`03O01oog`000Uoo`004Woo00<007ooOol0MWoo00Al07ooOoml009oo`03O01oogoo
00Ioo`03O01oogoo00Ioo`03O01oogoo00Qoo`004Woo00<007ooOol0Mgoo00=l07ooO0000goo00=l
07ooOol00Woo1g`01Goo00=l07ooOol027oo000BOol00`00Oomoo`1hOol3O002Ool00g`0Oomoo`05
Ool00g`0Oomoo`06Ool2O009Ool0019oo`03001oogoo07Yoo`Al00Moo`03O01oogoo00Eoo`9l0003
Ooml07oo00Moo`004Woo00<007ooOol0Ngoo00=l07ooOol01goo00=l07ooOol04Goo000BOol00`00
Oomoo`1lOol2O00KOol0019oo`03001oogoo07ioo`9l01Uoo`004Woo00<007ooOol0P7oo0W`05goo
000BOol00`00Oomoo`22Ool00g`0Oomoo`0DOol0019oo`03001oogoo08=oo`9l01Aoo`004Woo00<0
07ooOol0QGoo00=l07ooOol04Goo000BOol00`00Oomoo`26Ool2O00AOol0019oo`03001oogoo08Qo
o`03O01oogoo00ioo`004Woo00<007ooOol0RGoo00=l07ooOol03Goo000BOol00`00Oomoo`2:Ool0
0g`0Oomoo`0<Ool0019oo`03001oogoo08]oo`9l00aoo`004Woo00<007ooOol0SGoo00=l07ooOol0
2Goo000BOol00`00Oomoo`2>Ool00g`0Oomoo`08Ool0019oo`03001oogoo08moo`9l00Qoo`004Woo
00<007ooOol0TGoo00=l07ooOol01Goo000BOol00`00Oomoo`2BOol2O005Ool0019oo`03001oogoo
09Aoo`03O01oogoo009oo`004Woo00<007ooOol0VGoo000BOol00`00Oomoo`2IOol0019oo`03001o
ogoo09Uoo`004Woo00<007ooOol0VGoo000BOol00`00Oomoo`2IOol00:ioo`00[Woo002^Ool00:io
o`00[Woo002^Ool00:ioo`00[Woo002^Ool00:ioo`00\
\>"],
  ImageRangeCache->{{{142.875, 281.375}, {659.625, 465.375}} -> {-3.254, \
5.93741, 0.0165374, 0.0118124}}],

Cell[TextData[{
  "Beweis:\n",
  StyleBox["Aus  ",
    FontFamily->"Times New Roman"],
  StyleBox["x",
    FontFamily->"Times New Roman",
    FontSlant->"Italic"],
  StyleBox[" > 0  folgt mit 2.1  ",
    FontFamily->"Times New Roman"],
  Cell[BoxData[
      \(TraditionalForm\`a < a + x\)],
    FontFamily->"Times New Roman"],
  StyleBox[" und mit 2.4  ",
    FontFamily->"Times New Roman"],
  Cell[BoxData[
      FormBox[
        StyleBox[\(a\/b\),
          FontSize->14], TraditionalForm]],
    FontFamily->"Times New Roman"],
  StyleBox[" <",
    FontFamily->"Times New Roman"],
  Cell[BoxData[
      FormBox[
        StyleBox[\(\(a\  + \ x\)\/b\),
          FontSize->14], TraditionalForm]],
    FontFamily->"Times New Roman"],
  StyleBox[".\n\nWird nun  ",
    FontFamily->"Times New Roman"],
  StyleBox["a",
    FontFamily->"Times New Roman",
    FontSlant->"Italic"],
  StyleBox["  durch  ",
    FontFamily->"Times New Roman"],
  StyleBox["a \[Dash]",
    FontFamily->"Times New Roman",
    FontSlant->"Italic"],
  StyleBox[" ",
    FontFamily->"Times New Roman"],
  StyleBox["x",
    FontFamily->"Times New Roman",
    FontSlant->"Italic"],
  StyleBox["  ersetzt, so folgt  ",
    FontFamily->"Times New Roman"],
  Cell[BoxData[
      FormBox[
        StyleBox[\(\(a\  - \ x\)\/b\),
          FontSize->14], TraditionalForm]],
    FontFamily->"Times New Roman"],
  StyleBox["<",
    FontFamily->"Times New Roman"],
  Cell[BoxData[
      FormBox[
        StyleBox[\(\(\((a\  - \ x)\)\  + \ x\)\/b\),
          FontSize->14], TraditionalForm]],
    FontFamily->"Times New Roman"],
  StyleBox[" =",
    FontFamily->"Times New Roman"],
  Cell[BoxData[
      \(TraditionalForm\`a\/b\)],
    FontFamily->"Times New Roman",
    FontSize->14],
  StyleBox[".\n",
    FontFamily->"Times New Roman"]
}], "Text",
  FontFamily->"Arial"],

Cell[TextData[{
  "6.\tEs seien  ",
  Cell[BoxData[
      \(TraditionalForm\`a, b, x > 0\)]],
  " . \n\tDann gilt  ",
  Cell[BoxData[
      FormBox[
        StyleBox[\(a\/\(b\  + \ x\)\),
          FontSize->14], TraditionalForm]]],
  "<",
  Cell[BoxData[
      \(TraditionalForm\`a\/b\)],
    FontSize->14],
  " und falls noch  ",
  Cell[BoxData[
      \(TraditionalForm\`\(\(x\)\(<\)\(b\)\(\ \)\)\)]],
  " ist, gilt auch  ",
  Cell[BoxData[
      FormBox[
        RowBox[{
          StyleBox[\(a\/b\),
            FontSize->14], "<", 
          StyleBox[\(a\/\(b\  - \ x\)\),
            FontSize->14]}], TraditionalForm]]],
  "."
}], "Text",
  FontFamily->"Times New Roman"],

Cell[GraphicsData["PostScript", "\<\
%!
%%Creator: Mathematica
%%AspectRatio: .61803 
MathPictureStart
/Mabs {
Mgmatrix idtransform
Mtmatrix dtransform
} bind def
/Mabsadd { Mabs
3 -1 roll add
3 1 roll add
exch } bind def
%% Graphics
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12  scalefont  setfont
% Scaling calculations
0.0238095 0.31746 0 0.123607 [
[.34127 -0.0125 -5 -15.6875 ]
[.34127 -0.0125 5 0 ]
[.65873 -0.0125 -5 -15.6875 ]
[.65873 -0.0125 5 0 ]
[.01131 .0618 -16.1875 -12.0625 ]
[.01131 .0618 0 12.0625 ]
[ 0 0 0 0 ]
[ 1 .61803 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
0 g
.25 Mabswid
[ ] 0 setdash
.34127 0 m
.34127 .00625 L
s
gsave
.34127 -0.0125 -66 -19.6875 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(a) show
69.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
.65873 0 m
.65873 .00625 L
s
gsave
.65873 -0.0125 -66 -19.6875 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 23.6875 translate 1 -1 scale
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
63.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(b) show
69.000 15.813 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
/Times-Italic findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
0 0 m
1 0 L
s
.02381 .0618 m
.03006 .0618 L
s
gsave
.01131 .0618 -77.1875 -16.0625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 32.125 translate 1 -1 scale
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding WindowsANSIEncoding def
        currentdict
    end

    newfontname exch definefont pop
} def
63.000 18.625 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
%%BeginResource: font Times-Italic-MISO
%%BeginFont: Times-Italic-MISO
/Times-Italic /Times-Italic-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
66.063 10.375 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(a) show
%%IncludeResource: font Math1
%%IncludeFont: Math1
/Math1 findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
64.750 18.625 moveto
(\\200\\200) show
68.250 18.625 moveto
(\\200\\200) show
71.438 18.625 moveto
(\\200) show
66.063 27.063 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
(b) show
75.188 18.625 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
.02381 0 m
.02381 .61803 L
s
0 0 m
1 0 L
1 .61803 L
0 .61803 L
closepath
clip
newpath
0 0 0 r
1.5 Mabswid
.02381 .0618 m
.04955 .0618 L
.07763 .0618 L
.104 .0618 L
.12936 .0618 L
.15635 .0618 L
.18233 .0618 L
.20995 .0618 L
.23655 .0618 L
.26215 .0618 L
.28938 .0618 L
.3156 .0618 L
.34081 .0618 L
.36766 .0618 L
.39349 .0618 L
.42096 .0618 L
.44742 .0618 L
.47287 .0618 L
.49995 .0618 L
.52603 .0618 L
.55373 .0618 L
.58043 .0618 L
.60612 .0618 L
.63344 .0618 L
.65841 .0618 L
s
1 0 0 r
.02381 .0618 m
.04955 .06442 L
.07763 .06753 L
.104 .07074 L
.12936 .07413 L
.15635 .07811 L
.18233 .08237 L
.20995 .08744 L
.23655 .09295 L
.26215 .09895 L
.28938 .10624 L
.3156 .11436 L
.34081 .12343 L
.36766 .13481 L
.39349 .14794 L
.42096 .16504 L
.44742 .1857 L
.47287 .21113 L
.49995 .24714 L
.52603 .2957 L
.54029 .33132 L
.55373 .37373 L
.56711 .42831 L
.57942 .49478 L
.59197 .58774 L
s
.59197 .58774 m
.59504 .61803 L
s
0 0 1 r
.02381 .0618 m
.06244 .05826 L
.10458 .05483 L
.14415 .05196 L
.18221 .04946 L
.22272 .04706 L
.26171 .04496 L
.30316 .04292 L
.34309 .04112 L
.3815 .03953 L
.42237 .03797 L
.46172 .03658 L
.49955 .03533 L
.53984 .03409 L
.57861 .03298 L
.61984 .03188 L
.65954 .03088 L
.69774 .02998 L
.73838 .02908 L
.77751 .02826 L
.81909 .02744 L
.85916 .02669 L
.89771 .02601 L
.93871 .02532 L
.97619 .02472 L
s
0 0 0 r
.02381 .0618 m
.06244 .0618 L
.10458 .0618 L
.14415 .0618 L
.18221 .0618 L
.22272 .0618 L
.26171 .0618 L
.30316 .0618 L
.34309 .0618 L
.3815 .0618 L
.42237 .0618 L
.46172 .0618 L
.49955 .0618 L
.53984 .0618 L
.57861 .0618 L
.61984 .0618 L
.65954 .0618 L
.69774 .0618 L
.73838 .0618 L
.77751 .0618 L
.81909 .0618 L
.85916 .0618 L
.89771 .0618 L
.93871 .0618 L
.97619 .0618 L
s
1 0 0 r
gsave
.5 .49443 -78.0938 -16.0625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 32.125 translate 1 -1 scale
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding WindowsANSIEncoding def
        currentdict
    end

    newfontname exch definefont pop
} def
63.000 18.625 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
%%BeginResource: font Times-Italic-MISO
%%BeginFont: Times-Italic-MISO
/Times-Italic /Times-Italic-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
75.063 10.375 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
(a) show
%%IncludeResource: font Math1
%%IncludeFont: Math1
/Math1 findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
64.750 18.625 moveto
(\\200\\200\\200\\200\\200\\200\\200\\200) show
78.750 18.625 moveto
(\\200\\200\\200\\200) show
85.750 18.625 moveto
(\\200\\200) show
89.438 18.625 moveto
(\\200) show
66.063 27.063 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
(b) show
74.438 27.063 moveto
%%IncludeResource: font Math1
%%IncludeFont: Math1
/Math1 findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
(-) show
84.813 27.063 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
(x) show
93.188 18.625 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
1.000 0.000 0.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
0 0 1 r
gsave
.88095 .13597 -78.0938 -16.0625 Mabsadd m
1 1 Mabs scale
currentpoint translate
0 32.125 translate 1 -1 scale
/MISOfy
{
    /newfontname exch def
    /oldfontname exch def

    oldfontname findfont
    dup length dict begin
        {1 index /FID ne {def} {pop pop} ifelse} forall
        /Encoding WindowsANSIEncoding def
        currentdict
    end

    newfontname exch definefont pop
} def
63.000 18.625 moveto
%%IncludeResource: font Times-Italic
%%IncludeFont: Times-Italic
%%BeginResource: font Times-Italic-MISO
%%BeginFont: Times-Italic-MISO
/Times-Italic /Times-Italic-MISO MISOfy
%%EndFont
%%EndResource
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
0.000 0.000 rmoveto
75.063 10.375 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
(a) show
%%IncludeResource: font Math1
%%IncludeFont: Math1
/Math1 findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
64.750 18.625 moveto
(\\200\\200\\200\\200\\200\\200\\200\\200) show
78.750 18.625 moveto
(\\200\\200\\200\\200) show
85.750 18.625 moveto
(\\200\\200) show
89.438 18.625 moveto
(\\200) show
66.063 27.063 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
(b) show
74.438 27.063 moveto
%%IncludeResource: font Math1
%%IncludeFont: Math1
/Math1 findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
(+) show
84.813 27.063 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
(x) show
93.188 18.625 moveto
%%IncludeResource: font Times-Italic-MISO
%%IncludeFont: Times-Italic-MISO
/Times-Italic-MISO findfont 12.000 scalefont
[1 0 0 -1 0 0 ] makefont setfont
0.000 0.000 1.000 setrgbcolor
0.000 0.000 rmoveto
1.000 setlinewidth
grestore
% End of Graphics
MathPictureEnd
\
\>"], "Graphics",
  ImageSize->{218.25, 134.688},
  ImageMargins->{{98.8125, 0}, {0, 0}},
  ImageRegion->{{0, 1}, {0, 1}},
  ImageCache->GraphicsData["Bitmap", "\<\
CF5dJ6E]HGAYHf4PAg9QL6QYHg<PAVmbKF5d0`40003J0000QQ000`40O003h00OfWoo003JOol00=Yo
o`00fWoo003JOol0059oo`800003Ool0000003Qoo`8004Uoo`00DWoo00@007oo000003Qoo`04001o
ogoo0018Ool0059oo`04001oogoo000hOol01@00Oomoogoo0000Agoo001BOol01@00Oomoogoo0000
>7oo00@007ooOol004Moo`00Dgoo00@007ooOol003Qoo`800003Ool007oo04Ioo`00E7oo0`00>7oo
00@007oo000004Moo`00Sgoo00<007ooOol0B7oo002@Ool00`00Oomoo`17Ool008moo`8004Uoo`00
fWoo003JOol00=Yoo`00fWoo000FOonl0008Ool000ioo`8000Yoo`03001oogoo03Qoo`03001oogoo
03Uoo`03001oogoo04Ioo`003Goo00@007ooOol000Uoo`03001oogoo0;eoo`003Goo00D007ooOomo
o`0000Qoo`03001oogoo0;eoo`003Woo00@007ooOol000Qoo`03001oogoo0:aoo`@07`eoo`003Woo
0P0000=oo`00Ool01goo00<007ooOol0N7oo=00O4Goo000>Ool01000Ool0000027oo00<007ooOol0
Dgoo9@0OAGoo000>Ool00`00Oomoo`09Ool00`00Oomoo`0mOolF01mZOol000moo`03001oogoo00Qo
o`03001oogoo02MooaH07h1oo`003Woo0P002Woo00<007ooOol067oo3`0OUWoo000JOol00`00Oomo
o`09Ool?01nUOol001Yook<000eoo`006Woo00<007ooOol02W`0/goo000;Ool90006Ool00`00Oomo
o`0:Ool5O02^Ool001Yoo`03001oogoo00moo`Yl0:Aoo`006Woo00<007ooOol06Goo1G`0M7oo0P0O
2Woo00<07gooOol00goo00@07gooOol07aEoo`006Woo00<007ooOol07Woo1G`0KWoo00@07gooOol0
7`Uoo`0301moogoo00Aoo`0301moo`0O01Eoo`006Woo00<007ooOol08goo1G`0JGoo00D07gooOomo
o`0O00Qoo`0301moogoo00Eoo`0301moogoo01Aoo`003Goo0P0000=oo`00000027oo00<007ooOol0
:7oo17`0IWoo00@07gooOol07`Eoo`L07`Aoo`0301moogoo01Aoo`003Goo00@007oo000000Uoo`03
001oogoo02aoo`9l06Aoo`807`03Ool07goo00Moo`0301moogoo00Eoo`807aEoo`003Goo00@007oo
Ool000Uoo`03001oogoo02ioo`Al061oo`0401moo`0O01l8Ool00`0OOomoo`04Ool201l00goo01mo
o`0COol000eoo`05001oogooOol00008Ool00`00Oomoo`0bOol3O01MOol00`0OOomoo`09Ool00`0O
Oomoo`0LOol000ioo`04001oogoo0008Ool00`00Oomoo`0eOol2O01LOol00`0OOomoo`0WOol000mo
o`<000Qoo`03001oogoo03Moo`=l05Qoo`807bUoo`006Woo00<007ooOol0>Woo0W`0PGoo000JOol0
0`00Oomoo`0lOol2O01oOol001Yoo`03001oogoo03ioo`9l07eoo`006Woo00<007ooOol0@7oo0W`0
CWoo6`0O4Woo000JOol00`00Oomoo`12Ool00g`0Oomoo`1hOol001Yoo`03001oogoo04=oo`9l07Qo
o`006Woo00<007ooOol0AGoo0W`0MWoo000JOol00`00Oomoo`17Ool00g`0Oomoo`1cOol001Yoo`03
001oogoo04Qoo`03O01oogoo04moo`807`03Ool07`0O01ioo`006Woo00<007ooOol0BGoo0W`0Cgoo
00@07goo01l07amoo`006Woo00<007ooOol0Bgoo00=l07ooOol0C7oo00@07gooOol07amoo`006Woo
00<007ooOol0C7oo00=l07ooOol0Bgoo00D07gooOomoo`0O01ioo`006Woo00<007ooOol0CGoo00=l
07ooOol0Bgoo00@07gooOol07aioo`006Woo00<007ooOol0CWoo0W`0C7oo0`0O7Woo000JOol00`00
Oomoo`1@Ool00g`0Oomoo`1ZOol001Yoo`03001oogoo055oo`03O01oogoo06Uoo`006Woo00<007oo
Ool0DWoo00=l07ooOol0J7oo000JOol00`00Oomoo`1BOol00g`0Oomoo`1XOol001Yoo`03001oogoo
05=oo`03O01oogoo06Moo`006Woo00<007ooOol0E7oo00=l07ooOol0IWoo000JOol00`00Oomoo`1E
Ool00g`0Oomoo`1UOol001Yoo`03001oogoo05Eoo`03O01oogoo06Eoo`006Woo00<007ooOol0EWoo
00=l07ooOol0I7oo000JOol00`00Oomoo`1GOol00g`0Oomoo`1SOol001Yoo`03001oogoo05Moo`03
O01oogoo06=oo`006Woo00<007ooOol0F7oo00=l07ooOol0HWoo000JOol00`00Oomoo`1HOol00g`0
Oomoo`1ROol001Yoo`03001oogoo05Uoo`03O01oogoo065oo`006Woo00<007ooOol0FGoo00=l07oo
Ool0HGoo000JOol00`00Oomoo`1JOol00g`0Oomoo`1POol001Yoo`03001oogoo05Yoo`03O01oogoo
061oo`006Woo00<007ooOol0Fgoo00=l07ooOol0Ggoo000JOol00`00Oomoo`1KOol00g`0Oomoo`1O
Ool001Yoo`03001oogoo05aoo`03O01oogoo05ioo`006Woo00<007ooOol0G7oo00=l07ooOol0GWoo
000JOol00`00Oomoo`1MOol00g`0Oomoo`1MOol001Yoo`03001oogoo05eoo`03O01oogoo05eoo`00
6Woo00<007ooOol0GWoo00=l07ooOol0G7oo000JOol00`00Oomoo`1NOol00g`0Oomoo`1LOol001Yo
o`03001oogoo05ioo`03O01oogoo05aoo`006Woo00<007ooOol0GWoo00=l07ooOol0G7oo000JOol0
0`00Oomoo`1OOol00g`0Oomoo`1KOol001Yoo`03001oogoo05moo`03O01oogoo05]oo`006Woo00<0
07ooOol0Ggoo00=l07ooOol0Fgoo000JOol00`00Oomoo`1OOol00g`0Oomoo`1KOol001Yoo`03001o
ogoo061oo`03O01oogoo05Yoo`006Woo00<007ooOol0H7oo00=l07ooOol0FWoo000JOol00`00Oomo
o`1POol00g`0Oomoo`1JOol001Yoo`03001oogoo065oo`03O01oogoo05Uoo`006Woo00<007ooOol0
HGoo00=l07ooOol0FGoo000JOol00`00Oomoo`1QOol00g`0Oomoo`1IOol001Yoo`03001oogoo065o
o`03O01oogoo05Uoo`006Woo00<007ooOol0HWoo00=l07ooOol0F7oo000JOol00`00Oomoo`1ROol0
0g`0Oomoo`1HOol001Yoo`03001oogoo069oo`03O01oogoo05Qoo`006Woo00<007ooOol0Hgoo00=l
07ooOol0Egoo000JOol00`00Oomoo`1SOol00g`0Oomoo`1GOol001Yoo`03001oogoo06=oo`03O01o
ogoo05Moo`006Woo00<007ooOol0Bgoo0W`047oo00Al07ooOoml009oo`03O01oogoo05Moo`006Woo
00<007ooOol0BWoo00Al07ooOoml011oo`03O01oog`0009oo`03O01oogoo05Moo`006Woo00<007oo
Ool0BWoo00El07ooOomoog`0011oo`03O01oogoo009oo`03O01oogoo05Ioo`006Woo00<007ooOol0
Bgoo00Al07ooOoml00Eoo`Ml00Aoo`03O01oogoo009oo`03O01oogoo05Ioo`006Woo00<007ooOol0
Bgoo0W`000=oog`0Ool03goo0W`00goo00=l07ooOol0EWoo000JOol00`00Oomoo`1;Ool017`0Ooml
07`03goo0W`000Eoog`0Oomoog`005Qoo`006Woo00<007ooOol0Bgoo00=l07ooOol05Woo00=l07oo
Ool0EWoo000JOol00`00Oomoo`1<Ool00g`0Oomoo`0EOol00g`0Oomoo`1FOol001Yoo`03001oogoo
04]oo`9l01Qoo`03O01oogoo05Eoo`006Woo00<007ooOol0IGoo00=l07ooOol0EGoo000JOol00`00
Oomoo`1UOol00g`0Oomoo`1EOol001Yoo`03001oogoo06Eoo`03O01oogoo05Eoo`006Woo00<007oo
Ool0BGoo6g`000=oog`0Ool0EWoo000JOol00`00Oomoo`1UOol00g`0Oomoo`1EOol001Yoo`03001o
ogoo06Eoo`03O01oogoo05Eoo`006Woo00<007ooOol0IWoo00=l07ooOol0E7oo000JOol00`00Oomo
o`1VOol00g`0Oomoo`1DOol001Yoo`03001oogoo05=oo`9l0003Ooml07`000ioo`03O01oogoo05Ao
o`006Woo00<007ooOol0Dgoo00Al07ooO01l00moo`03O01oogoo05Aoo`006Woo00<007ooOol0Dgoo
00Al07ooOoml00moo`03O01oogoo05Aoo`006Woo00<007ooOol0Dgoo00El07ooOomoog`000ioo`03
O01oogoo05Aoo`006Woo00<007ooOol0E7oo00Al07ooOoml00ioo`03O01oogoo05Aoo`006Woo00<0
07ooOol0EGoo0g`03Woo00=l07ooOol0E7oo000JOol00`00Oomoo`1VOol00g`0Oomoo`1DOol001Yo
o`03001oogoo06Moo`03O01oogoo05=oo`006Woo00<007ooOol0Igoo00=l07ooOol0Dgoo000JOol0
0`00Oomoo`1WOol00g`0Oomoo`1COol001Yoo`03001oogoo06Moo`03O01oogoo05=oo`006Woo00<0
07ooOol0Igoo00=l07ooOol0Dgoo000JOol00`00Oomoo`1WOol00g`0Oomoo`1COol001Yoo`03001o
ogoo06Moo`03O01oogoo05=oo`006Woo00<007ooOol0J7oo00=l07ooOol0DWoo000JOol00`00Oomo
o`1XOol00g`0Oomoo`1BOol001Yoo`03001oogoo06Qoo`03O01oogoo059oo`00\
\>"],
  ImageRangeCache->{{{135.25, 308.813}, {226, 119.25}} -> {-3.3002, 5.67689, \
0.0168679, 0.0433218}}],

Cell[TextData[{
  "Beweis:\n\n\t\t",
  Cell[BoxData[GridBox[{
          {
            StyleBox["0",
              FontFamily->"Times New Roman",
              FontSize->10], 
            StyleBox["<",
              FontFamily->"Times New Roman",
              FontSize->10], 
            StyleBox["x",
              FontFamily->"Times New Roman",
              FontSize->10,
              FontSlant->"Italic"], 
            StyleBox[" ",
              FontFamily->"Times New Roman"]},
          {
            StyleBox["b",
              FontFamily->"Times New Roman",
              FontSize->10,
              FontSlant->"Italic"], 
            StyleBox["<",
              FontFamily->"Times New Roman",
              FontSize->10], 
            StyleBox[
              RowBox[{
                StyleBox["b",
                  FontFamily->"Times New Roman",
                  FontSlant->"Italic"], 
                StyleBox["+",
                  FontFamily->"Times New Roman",
                  FontSlant->"Plain"], 
                StyleBox["x",
                  FontFamily->"Times New Roman",
                  FontSlant->"Italic"]}],
              FontFamily->"Arial",
              FontSize->10], 
            StyleBox[\(\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\(2.1\)\),
              FontFamily->"Times New Roman",
              FontSize->10]},
          {
            StyleBox[
              FractionBox["1", 
                RowBox[{
                  StyleBox["b",
                    FontSlant->"Italic"], 
                  StyleBox[" ",
                    FontSlant->"Italic"], 
                  StyleBox["+",
                    FontSlant->"Plain"], 
                  StyleBox[" ",
                    FontSlant->"Plain"], 
                  StyleBox["x",
                    FontSlant->"Italic"]}]],
              FontFamily->"Times New Roman",
              FontSize->12], 
            StyleBox["<",
              FontFamily->"Times New Roman",
              FontSize->10], 
            StyleBox[
              FractionBox[
                StyleBox["1",
                  FontSlant->"Plain"], "b"],
              FontFamily->"Times New Roman",
              FontSize->12,
              FontSlant->"Italic"], 
            StyleBox[\(\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\(2.4\)\),
              FontFamily->"Times New Roman",
              FontSize->10]},
          {
            StyleBox[
              FractionBox[
                StyleBox["a",
                  FontSlant->"Italic"], 
                RowBox[{
                  StyleBox["b",
                    FontSlant->"Italic"], 
                  StyleBox[" ",
                    FontSlant->"Italic"], 
                  StyleBox["+",
                    FontSlant->"Plain"], 
                  StyleBox[" ",
                    FontSlant->"Plain"], 
                  StyleBox["x",
                    FontSlant->"Italic"]}]],
              FontFamily->"Times New Roman",
              FontSize->12], 
            StyleBox["<",
              FontFamily->"Times New Roman",
              FontSize->10], 
            StyleBox[\(a\/b\),
              FontFamily->"Times New Roman",
              FontSize->12,
              FontSlant->"Italic"], 
            StyleBox[\(\(\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \)\(2.2\)\),
              FontFamily->"Times New Roman",
              FontSize->10]}
          }]],
    FontSize->14],
  "\n\t\n",
  StyleBox["Damit ist der erste Teil bewiesen. \nDer zweite folgt wieder \
durch Ersetzung von  ",
    FontFamily->"Times New Roman"],
  StyleBox["b",
    FontFamily->"Times New Roman",
    FontSlant->"Italic"],
  StyleBox["  durch  ",
    FontFamily->"Times New Roman"],
  StyleBox["b",
    FontFamily->"Times New Roman",
    FontSlant->"Italic"],
  StyleBox[" \[Dash]",
    FontFamily->"Times New Roman"],
  StyleBox[" x",
    FontFamily->"Times New Roman",
    FontSlant->"Italic"],
  StyleBox[" :\n\t",
    FontFamily->"Times New Roman"],
  Cell[BoxData[
      FormBox[
        RowBox[{
          StyleBox[\(a\/b\),
            FontSize->14], "=", 
          RowBox[{
            StyleBox[\(a\/\(\((b\  - \ x)\)\  + \ x\)\),
              FontSize->14], "<", 
            StyleBox[\(a\/\(b\  - \ x\)\),
              FontSize->14]}]}], TraditionalForm]],
    FontFamily->"Times New Roman",
    FontSize->12],
  StyleBox[" .",
    FontFamily->"Times New Roman",
    FontSize->12],
  StyleBox["\n\t",
    FontSlant->"Italic"]
}], "Text",
  FontFamily->"Arial",
  FontSize->10],

Cell[TextData[{
  StyleBox["Warum sind Ungleichungen in der Analysis so wichtig?\n",
    FontFamily->"Arial",
    FontSize->12,
    FontVariations->{"Underline"->True}],
  StyleBox["\n",
    FontFamily->"Arial",
    FontSize->12],
  StyleBox["Es k\[ODoubleDot]nnen mit ihnen Gleichungen bewiesen werden!",
    FontFamily->"Arial",
    FontSize->12,
    FontVariations->{"Underline"->True}],
  StyleBox["\n",
    FontSize->12,
    FontColor->RGBColor[0, 1, 0]],
  StyleBox["\n",
    FontWeight->"Bold"],
  StyleBox["Der einfache Fall ist: Es sei  ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["a",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox[" \[LessEqual] ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["b",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox["  und  ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["b",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox[" \[LessEqual] ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["a",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox[" . Dann ist  ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["a",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox[" = ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["b",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox[" .\n\nDer wichtige Fall ist:  \n",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["a",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox["  und  ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["b",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox["  \"unterscheiden sich um beliebig wenig\". Dann ist  ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["a",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox[" = ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["b",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox[" . \n\nDoch was hei\[SZ]t \"unterscheiden sich beliebig wenig\"? \
Es hei\[SZ]t: Der Betrag der Differenz von  ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["a",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox["  und  ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["b",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox["  ist kleiner als jede positive Zahl  ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["c",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox[" .\n\n",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["Beweis:\n",
    FontFamily->"Arial",
    FontSize->10],
  StyleBox["1. Fall: ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["a",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox[" = ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["b",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox[" . Fertig! 2. Fall:",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox[" a ",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox["\[NotEqual]",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox[" b",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox[" . O.B.d.A. sei  ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["a",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox[" > ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["b . ",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox["Es gelte also f\[UDoubleDot]r jedes  ",
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["c",
    FontFamily->"Times New Roman",
    FontSize->10,
    FontSlant->"Italic"],
  StyleBox[" > 0 , dass  ",
    FontFamily->"Times New Roman",
    FontSize->10],
  Cell[BoxData[
      \(TraditionalForm\`a - b < c\)],
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["  und damit auch  ",
    FontFamily->"Times New Roman",
    FontSize->10],
  Cell[BoxData[
      \(TraditionalForm\`0 < a - b < c\)],
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox[" . \nWenn das f\[UDoubleDot]r jedes ",
    FontFamily->"Times New Roman",
    FontSize->10],
  Cell[BoxData[
      \(TraditionalForm\`c > 0\)],
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox[" gilt, dann gilt es insbesondere f\[UDoubleDot]r  ",
    FontFamily->"Times New Roman",
    FontSize->10],
  Cell[BoxData[
      FormBox[
        RowBox[{\(c\_1\), ":=", 
          StyleBox[\(\(a - b\)\/2\),
            FontSize->12]}], TraditionalForm]],
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox[" , was nach A 2 und 2.4 auch positiv ist. Damit folgt ",
    FontFamily->"Times New Roman",
    FontSize->10],
  Cell[BoxData[
      FormBox[
        RowBox[{\(0 < a - b < c\_1\), "=", 
          StyleBox[\(\(a - b\)\/2\),
            FontSize->12]}], TraditionalForm]],
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox[" , und nach Multiplikation mit ",
    FontFamily->"Times New Roman",
    FontSize->10],
  Cell[BoxData[
      FormBox[
        StyleBox[\(1\/\(a - b\)\),
          FontSize->12], TraditionalForm]],
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox["(> 0 , da ",
    FontFamily->"Times New Roman",
    FontSize->10],
  Cell[BoxData[
      \(TraditionalForm\`a - b > 0\)],
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox[" ) , dass ",
    FontFamily->"Times New Roman",
    FontSize->10],
  Cell[BoxData[
      FormBox[
        StyleBox[\(1\/2\),
          FontSize->12], TraditionalForm]],
    FontFamily->"Times New Roman",
    FontSize->10],
  StyleBox[">",
    FontSize->10],
  StyleBox[" 1 , also ein Widerspruch.",
    FontFamily->"Times New Roman",
    FontSize->10]
}], "Text",
  FontSize->9]
}, Open  ]]
},
FrontEndVersion->"4.1 for Microsoft Windows",
ScreenRectangle->{{0, 1024}, {0, 695}},
WindowSize->{493, 668},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
PrintingCopies->1,
PrintingPageRange->{Automatic, Automatic},
PageHeaders->{{Inherited, Inherited, Inherited}, {Cell[ 
        TextData[ "0.7: Die Anordnung der reellen Zahlen"], "Header"], 
      Inherited, Inherited}},
PageFooters->{{Inherited, Inherited, Inherited}, {Cell[ 
        TextData[ 
        "Materialien zur Vorlesung Elementare Analysis, Wintersemester 2003 / \
4"]], Inherited, Inherited}},
PageFooterLines->{Inherited, True},
PrintingOptions->{"FirstPageHeader"->False},
Magnification->1
]

(*******************************************************************
Cached data follows.  If you edit this Notebook file directly, not
using Mathematica, you must remove the line containing CacheID at
the top of  the file.  The cache data will then be recreated when
you save this file from within Mathematica.
*******************************************************************)

(*CellTagsOutline
CellTagsIndex->{}
*)

(*CellTagsIndex
CellTagsIndex->{}
*)

(*NotebookFileOutline
Notebook[{

Cell[CellGroupData[{
Cell[1727, 52, 51, 0, 59, "Section"],
Cell[1781, 54, 153, 5, 28, "SmallText"],
Cell[1937, 61, 224, 6, 71, "Text"],
Cell[2164, 69, 4273, 179, 46, 2836, 156, "GraphicsData", "PostScript", \
"Graphics"],
Cell[6440, 250, 460, 15, 52, "Text"],
Cell[6903, 267, 15374, 508, 141, 10003, 437, "GraphicsData", "PostScript", \
"Graphics"],
Cell[22280, 777, 436, 18, 33, "Text"],
Cell[22719, 797, 7069, 267, 45, 4914, 235, "GraphicsData", "PostScript", \
"Graphics"],
Cell[29791, 1066, 796, 27, 128, "Text"],
Cell[30590, 1095, 6961, 252, 53, 3996, 211, "GraphicsData", "PostScript", \
"Graphics"],
Cell[37554, 1349, 393, 15, 52, "Text"],
Cell[37950, 1366, 236, 9, 54, "Text"],
Cell[38189, 1377, 209, 4, 40, "Text"],
Cell[38401, 1383, 5896, 243, 514, "Text"],
Cell[44300, 1628, 7413, 296, 583, "Text"],
Cell[51716, 1926, 654, 26, 60, "Text"],
Cell[52373, 1954, 19333, 554, 201, 9791, 432, "GraphicsData", "PostScript", \
"Graphics"],
Cell[71709, 2510, 1832, 64, 90, "Text"],
Cell[73544, 2576, 677, 26, 44, "Text"],
Cell[74224, 2604, 16290, 541, 114, 10298, 463, "GraphicsData", "PostScript", \
"Graphics"],
Cell[90517, 3147, 4487, 137, 187, "Text"],
Cell[95007, 3286, 6467, 236, 261, "Text"]
}, Open  ]]
}
]
*)



(*******************************************************************
End of Mathematica Notebook file.
*******************************************************************)