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'necessary and sufficient'
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| Title of object: |
necessary and sufficient |
| Canonical Name: |
NecessaryAndSufficient |
| Type: |
Definition |
| Created on: |
2006-07-29 14:09:57 |
| Modified on: |
2007-04-27 14:34:23 |
| Classification: |
msc:03B05 |
| Defines: |
necessary, necessity, sufficient, sufficiency |
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:
The statement ``$p$ is {\sl necessary\/} for $q$'' \PMlinkescapetext{means} ``$q$ \PMlinkname{implies}{Implication} $p$''.
The statement ``$p$ is {\sl sufficient\/} for $q$'' \PMlinkescapetext{means} ``$p$ \PMlinkname{implies}{Implication} $q$''.
The statement ``$p$ is {\sl necessary and sufficent\/} for $q$'' \PMlinkescapetext{means} ``$p$ \PMlinkname{if and only if}{Iff} $q$''.
For an example of how these \PMlinkescapetext{terms} are used in mathematics, see complete ultrametric field. |
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