even number
Definition Suppose k is an integer.
If there exists an integer r such that k=2r+1, then k is an odd number.
If there exists an integer r such that k=2r, then k is an even number.
The concept of even and odd numbers are most easily understood in the binary base. Then the above definition simply that even numbers end with a 0, and odd numbers end with a 1.
0.0.1 Properties
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1.
Every integer is either even or . This can be proven using induction, or using the fundamental theorem of arithmetic
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2.
An integer k is even () if and only if k2 is even ().
Title | even number |
Canonical name | EvenNumber |
Date of creation | 2013-03-22 13:56:29 |
Last modified on | 2013-03-22 13:56:29 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 10 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 11-00 |
Classification | msc 03-00 |
Related topic | NumberOdd |
Defines | odd number |
Defines | even integer |
Defines | odd integer |
Defines | even |
Defines | odd |