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### Are these numbers odd or even?

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Date: 27 Apr 1995 12:18:53 -0400
From: Anonymous
Subject: even or odd

Hi,

Would 2.5 be an even number, odd number, neither or both?  Also,
what about zero's evenness and/or oddness.  Infinity's?

Remember, time flies like an arrow, but fruit flies like a banana.
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Date: 27 Apr 1995 12:50:33 -0400
From: Dr. Ken
Subject: Re: even or odd

Hello there!

The concept of even and odd seems to be one of the few cases in math where
the intuition you learned in grade school will really hold true.  Evenness
and oddness only applies to the integers.  So we don't discuss whether 2.5
is even or odd; it's like asking which American state the Atlantic Ocean is
in, it just doesn't apply.  It's neither.

Zero, on the other hand, is very even.  It can be written in the form 2*n,
where n is an integer.  Odd numbers can be written in the form 2*n + 1.
Note that this lets you talk about whether negative numbers are even and odd.
-7 is odd, and -8 is even.  And since Infinity isn't an integer, it's also
neither even nor odd.

Thanks for the question!

-K
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Associated Topics:
Elementary Infinity