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'Zermelo's postulate'
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| Title of object: |
Zermelo's postulate |
| Canonical Name: |
ZermelosPostulate |
| Type: |
Theorem |
| Created on: |
2002-12-09 03:04:15 |
| Modified on: |
2002-12-09 03:08:26 |
| Classification: |
msc:03E25 |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
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% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
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%\usepackage{psfrag}
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%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
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Content:
If $\mathcal{F}$ is a disjoint family of nonempty sets, then there is a set $C$ which has exactly one element of each $A\in \mathcal{F}$ (i.e such that $A\cap C$ is a singleton for each $A\in \mathcal{F}$.)
This is one of the many propositions which are equivalent to the axiom of choice. |
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