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### Why Zero is neither Positive nor Negative

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Date: 10/5/95 at 22:5:27
From: Anonymous
Subject: Is 0 a negative or a positive?

Dear Dr. Math,

My class and I are wondering if 0 is a negative or a positive
number and why.  My name is David and I am in fifth grade at
Kyrene De La Sierra in Phoenix.

Sincerely,
Ms. Kieselbach's class
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Date: 10/6/95 at 16:16:32
From: Doctor Ken
Subject: Re: Is 0 a negative or a positive?

Hello!

Actually, zero is neither a negative or a positive number.  The
whole idea of positive and negative is defined in terms of zero.
Negative numbers are numbers that are smaller than zero, and
positive numbers are numbers that are bigger than zero.  Since
zero isn't bigger or smaller than itself (just like you're not
older than yourself, or taller than yourself), zero is neither
positive nor negative.

People sometimes talk about the "non-negative" numbers, and what
that means is all the numbers that aren't negative, in other words
all the positive numbers and zero.  So the only difference between
the set of positive numbers and the set of non-negative numbers is
that zero isn't in the first set, but it is in the second.
Similarly, the "non-positive" numbers are the negative numbers
together with zero.

-Doctor Ken,  The Geometry Forum

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