Talk:Even or odd: Difference between revisions

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== definition of even & odd numbers ==
This may be frivolous/trivial, but since the task is to determine if an integer is odd or even, a simple definition of an odd/even number could be in order.
 
<br>The definition (below) defines an ODD NUMBER, and goes further than limiting the definition to an ODD INTEGER:
<br><br>From MathWorld:
 
<br><br>An odd number is an integer of the form n=2k+1 where k is an integer.
 
<br><br>Integers which are not odd are called even.
<br><br>From MathWorld:
<br><br>The above definition has the advantage that it isn't dependent upon its (say, internal binary) representation (or any base, for that matter), although that is one method to determine evenness/oddness.
 
<br><br>I've also seen the definition that an odd number is an integer, that when divided by two, the absolute value of the remainder is (positive) unity.
<br><br>An &nbsp; ''odd number'' &nbsp; is an integer of the form &nbsp; '''n=2k+1''' &nbsp; where &nbsp; '''k''' &nbsp; is an integer.
<br>An even number ... the remainder is zero.
 
<br><br>Integers which are &nbsp; ''not odd'' &nbsp; are called &nbsp; ''even''.
 
 
<br><br>The above definition has the advantage that it isn't dependent upon its (say, internal binary) representation (or any base, for that matter), although that is one method to determine evenness/oddness.
 
<br><br>I've also seen the definition that an odd number is an integer, that when divided by two, the absolute value of the remainder is (positive) unity.
<br>AnFor an even number ... the remainder is zero.
 
<br>[[User:Gerard Schildberger|Gerard Schildberger]] 00:46, 16 March 2012 (UTC)