|
|
|
Viewing Version
5
of
'Bolzano-Weierstrass theorem'
|
[ view 'Bolzano-Weierstrass theorem'
|
back to history
]
| Title of object: |
Bolzano-Weierstrass theorem |
| Canonical Name: |
BolzanoWeierstrassTheorem |
| Type: |
Theorem |
| Created on: |
2002-02-18 19:43:40-05 |
| Modified on: |
2002-07-24 09:27:10.46542-04 |
| Classification: |
msc:40A05, msc:26A06 |
| Keywords: |
Bolzano-Weierstrass |
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:
Given any bounded, real sequence $(a_n)$ there exists a convergent subsequence $(a_{n_j})$.
More generally, any sequence $(a_n)$ in a compact set, has a convergent subsequence. |
|
|
|
|
|
