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### Is 0 a whole number?

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Date: 7/17/96 at 23:29:40
From: Lucas W Tolbert
Subject: Is 0 a whole number?

Is 0 a whole number?
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Date: 7/29/96 at 13:32:52
From: Doctor Jerry
Subject: Re: Is 0 a whole number?

What are whole numbers?  This term is rarely used by mathematicians.
It is used in teaching mathematics to young children, to distinguish
between whole and fractional numbers. The term whole number often is
used to mean the counting numbers, 1, 2, 3, .... Some would argue, I
suppose, that 0 is also a counting number. Others would disagree.

One starting point for the real number system is Peano's Postulates,
which amount to axioms for the positive integers. No mention is made
of 0. The number 0 emerges when, having defined addition for the set
of positive integers, one asks for solutions to equations of the form
m + x = n, where m and n are positive integers. So that such equations
can be solved, the set of positive integers is enlarged. The negative
numbers and 0 are created/constructed so that this equation can be
solved.

The rationals and reals can be created in a similar way.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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