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'even number'
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| Title of object: |
even number |
| Canonical Name: |
EvenNumber |
| Type: |
Definition |
| Created on: |
2003-09-05 15:11:23 |
| Modified on: |
2003-09-05 17:09:26 |
| Classification: |
msc:03-00, msc:11-00 |
| Defines: |
odd number, even integer, odd integer |
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
\newcommand{\sR}[0]{\mathbb{R}}
\newcommand{\sC}[0]{\mathbb{C}}
\newcommand{\sN}[0]{\mathbb{N}}
\newcommand{\sZ}[0]{\mathbb{Z}}
\renewcommand{\bibname}{References} |
Content:
{\bf Definition} Suppose $k$ is an integer.
If there exists an integer $r$ such that $k=2r+1$, then $k$ is an {\bf odd number}.
If there exists an integer $r$ such that $k=2r$, then $k$ is an {\bf even number}.
The concept of even and odd numbers are most easily understood in
the binary base. Then the above definition simply states that even numbers end
with a $0$, and odd numbers end with a $1$.
Using induction, or the fundamental theorem of arithmetic, one can prove that
every integer is either even or odd. |
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