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'numerable set'
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| Title of object: |
numerable set |
| Canonical Name: |
NumerableSet |
| Type: |
Definition |
| Created on: |
2006-06-20 15:05:21 |
| Modified on: |
2006-06-20 15:05:21 |
| Classification: |
msc:97A80 |
Revision comment (for changes between this and next version):
| Changes for correction #8442 ('extra word'). |
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
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Content:
A set $X$ is called numerable if there is a bijection $\mathbb{N}\to X$.
It is easy to show that $\mathbb{Z}$ and $\mathbb{Q}$ are numerable.
And it is a standard fact that the $\mathbb{R}$ is not numerable. |
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