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'non-isomorphic completions of $\mathbb{Q}$'
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| Title of object: |
non-isomorphic completions of $\mathbb{Q}$ |
| Canonical Name: |
NonIsomorphicCompletionsOfMathbbQ |
| Type: |
Theorem |
| Created on: |
2005-01-27 14:09:16 |
| Modified on: |
2005-01-27 14:09:16 |
| Classification: |
msc:13A18 |
| Defines: |
$p$-adic numbers |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here |
Content:
| No field $\mathbb{Q}_p$ of the {\em $p$-adic numbers} (\PMlinkname{$p$-adic rationals}{PAdicIntegers}) is isomorphic with the field $\mathbb{R}$ of the real numbers. |
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