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### Is Zero a Number?

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Date: 10/23/95 at 17:38:38
From: Anonymous
Subject: 0 as a number

I have been asking my students thinking questions such as, Why is 0 not
a number, or Why is 0 a number?  I have read your response to the
question about uses and functions of 0 but this doesn't explain to me
why 0 is classified as a whole number and not a natural number.  My
explanation is that natural numbers can be touched, whereas whole
numbers cannot be. Is it a whole number strictly by definition?
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Date: 11/1/95 at 11:34:1
From: Doctor Ken
Subject: Re: 0 as a number

Hello!

I think you're closest with your last explanation.  The natural numbers
are to be thought of as the "counting numbers."  They are 1,2,3,4,5,...,
i.e. the numbers you'd use to start counting a bunch of objects.  You
wouldn't use 0 to start counting, because if there are zero objects, you
don't count them.

To be honest, I never learned a nice way to think of the whole numbers,
but I think the best way is to think of them as "quantity numbers."
Someone could ask "how many pork chops do you have?," and then you could
answer with any "counting number," or if you don't have any pork chops,
you tell them "zero."  The set of numbers you can use to answer this
kind of question is the set of whole numbers.

With all this in mind, I would still say that zero is definitely a
number.  I would even say that -5 is a number, Sqrt{2}, Sqrt{-2}, 3+5i,
and Pi are all numbers.  It's just that some of them aren't certain
kinds of numbers.

To tell you the truth, I probably wouldn't try to shield kids from those
more exotic numbers either, because they can probably understand more
than most people think they can; we don't get smarter when we get older,
we just know more stuff.  But that's just my personal bias on the
matter.

-Doctor Ken,  The Geometry Forum
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Date: 09/30/2000 at 13:47:23
From: Franca Van Allen
Subject: Zero the hero

Dear Dr. Math,

I am a 5th grade teacher in Stockton California and I would like to add
to your answer. I tell my kids that Zero has many meanings:

1) By itself it may mean NOTHING, zero quantity.

2) In a place value setting it means that there is no amount in that
specific place.

3) Behind whole numbers it increases the whole number quantity by one
place value for each zero.

4) In the number line and in graphs it means THE POINT OF ORIGIN. All
numbers measure the distance from the point of origin, the bigger the
number, the farther the distance from zero. Also, zeroing in means to
get to the source, to target, to get to the point. What point? The
point of origin from which all numbers depart!

5) In geometry zero is a point. If we invent our own number system,
zero is any point we chose to begin.

6) In a binary system, where zero and one are the only two elements,
zero is "false" where one is "true." Binary systems make up our
computer language.

Kids are fascinated to learn all these facts about zero.

Thank you for your time,
Ms. Franca Van Allen
```
Associated Topics:
Middle School Number Sense/About Numbers

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