File:Steinitz numbers.pdf

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English:Hasse diagramof thelatticeofsupernatural numbers(Steinitz numbers). Bottom and top element are 1 and 0, respectively. Primes other than 2 and 3 are omitted for simplicity; true supernatural numbers form an infinite-dimensional, rather than a 2-dimensional,hypercube.The natural numbers, ordered by divisibility, are a sublattice of the supernatural numbers; they are obtained by removing the topmost and the rightmost points in this diagram, but keeping 0.
Date
Source Own work
Author Jochen Burghardt
Other versions File:Steinitz numbers.pdf-File:Steinitz numbers svg.svg
LaTeX source
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\textcolor{cNat}{\put(3.000,71.780){\makebox(0.000,0.000)[bl]{$81$}}}%

\textcolor{cNat}{\put(3.000,84.902){\makebox(0.000,0.000)[bl]{\Large\bf\vdots}}}%

\textcolor{cNat}{\put(203.000,203.000){\makebox(0.000,0.000)[bl]{$0$}}}%
\put(3.000,203.000){\makebox(0.000,0.000)[bl]{$3^\infty$}}%
\put(23.000,203.000){\makebox(0.000,0.000)[bl]{$2\!\cdot\!3^\infty$}}%
\put(41.000,203.000){\makebox(0.000,0.000)[bl]{$4\!\cdot\!3^\infty$}}%
\put(57.200,203.000){\makebox(0.000,0.000)[bl]{$8\!\cdot\!3^\infty$}}%
\put(71.780,203.000){\makebox(0.000,0.000)[bl]{$\mathbf{\ldots}$}}%

\put(203.000,3.000){\makebox(0.000,0.000)[bl]{$2^\infty$}}%
\put(203.000,23.000){\makebox(0.000,0.000)[bl]{$2^\infty\!\cdot\!3$}}%
\put(203.000,41.000){\makebox(0.000,0.000)[bl]{$2^\infty\!\cdot\!9$}}%
\put(203.000,57.200){\makebox(0.000,0.000)[bl]{$\mathbf{\vdots}$}}%
\end{picture}
\end{document}

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current07:25, 13 April 2020Thumbnail for version as of 07:25, 13 April 20201,297 × 1,268(41 KB)Jochen Burghardt(talk|contribs)highlighted natural numbers in green; larger ldots
08:14, 12 April 2020No thumbnail0 × 0(34 KB)Jochen Burghardt(talk|contribs)Uploaded own work with UploadWizard

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