File:Diagonal argument 01.pdf
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| Description |
English: An illustration of Cantor's diagonal argument (in base 2) for the existence of uncountable sets. The sequence at the bottom cannot occur anywhere in the enumeration of sequences above. (Adapted from File:Diagonal argument 2.svg; see File:Diagonal argument powerset.pdf for a similar version for power sets.) |
| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
| Other versions | File:Diagonal argument 01 svg.svg |
| LaTeX source Code |
|---|
\documentclass{article}
\usepackage[pdftex]{color}
\usepackage[paperwidth=50mm,paperheight=65mm]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{50mm}
\setlength{\textheight}{65mm}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0mm}
\definecolor{cPos} {rgb}{0.99,0.00,0.00}
\definecolor{cNeg} {rgb}{0.00,0.00,0.99}
\pagestyle{empty}
\newcommand{\0}[1]{\textcolor{cPos}{#1}}
\newcommand{\1}[1]{\textcolor{cNeg}{#1}}
\begin{document}
$\begin{array}{|*{14}{@{\;}c}|}
\hline
s_1 & = & \00 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \ldots \\ % periodic 0
s_2 & = & 1 & \01 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & \ldots \\ % periodic 1
s_3 & = & 0 & 1 & \00 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & \ldots \\ % periodic 0,1
s_4 & = & 1 & 0 & 1 & \00 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & \ldots \\ % periodic 1,0
s_5 & = & 1 & 1 & 0 & 1 & \00 & 1 & 1 & 0 & 1 & 0 & 1 & \ldots \\ % periodic 1,1,0,1,0
s_6 & = & 0 & 0 & 1 & 1 & 0 & \01 & 1 & 0 & 1 & 1 & 0 & \ldots \\ % 0, periodic 0,1,1
s_7 & = & 1 & 0 & 0 & 0 & 1 & 0 & \00 & 0 & 1 & 0 & 0 & \ldots \\ % periodic 1,0,0,0
s_8 & = & 0 & 0 & 1 & 1 & 0 & 0 & 1 & \01 & 0 & 0 & 1 & \ldots \\ % periodic 0,0,1,1
s_9 & = & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & \01 & 1 & 0 & \ldots \\ % periodic 1,1,0,0
s_{10} & = & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & \00 & 1 & \ldots \\ % binary numbers 1, 10, 11, 100, 101, ...)
s_{11} & = & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & \00 & \ldots \\ % 1 whenever new number starts in s_{10}
\vdots & & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \ddots \\
\hline
\multicolumn{10}{c}{} \\
\hline
s & = & \11 & \10 & \11 & \11 & \11 & \10 & \11 & \10 & \10 & \11 & \11 & \ldots \\
\hline
\end{array}$
\end{document}
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 10:07, 11 December 2013 |  | 293 × 383 (11 KB) | Jochen Burghardt (talk | contribs) | as suggested by RJGray on my EN talk page:"Try removing the commas (and perhaps spacing the 0s and 1s closer together?)" |
| 12:32, 10 December 2013 | No thumbnail | 0 × 0 (15 KB) | Jochen Burghardt (talk | contribs) | more enumeration elements, longer sequences | |
| 11:36, 10 December 2013 | No thumbnail | 0 × 0 (14 KB) | Jochen Burghardt (talk | contribs) | User created page with UploadWizard |
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