|
|
|
Viewing Version
3
of
'Zorn's lemma'
|
[ view 'Zorn's lemma'
|
back to history
]
| Title of object: |
Zorn's lemma |
| Canonical Name: |
ZornsLemma |
| Type: |
Theorem |
| Created on: |
2002-01-05 08:28:54 |
| Modified on: |
2002-02-03 12:53:44 |
| Classification: |
msc:03E25 |
| Keywords: |
Set theory |
Revision comment (for changes between this and next version):
| changes for correction #7241 |
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic} |
Content:
Let $X$ be a partially ordered set, and suppose that every chain in $X$ has an upper bound. Then $X$ has a maximal element $x$, in the sense that for all $y\in X$, $y\not> x$.
Zorn's lemma is equivalent to the axiom of choice. |
|
|
|
|
|
