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Is Zero a Number?

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?

Date: 11/1/95 at 11:34:1
From: Doctor Ken
Subject: Re: 0 as a number


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 

-Doctor Ken,  The Geometry Forum

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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