Do Natural Numbers Start with 0 or 1?

Date: 7/4/96 at 7:27:46
From: Anonymous
Subject: Natural Number Start with 0 or 1?

Hi Dr. Math!

Some of our 6-10 year olds learn that natural numbers are the numbers 
one uses for counting. As they never start counting with 0, when they 
enter the next school type they insist on their historic definition of 
the natural numbers and start with 1.

Which arguments would you give these 10-year-olds to convince them to 
start with 0?

Thanks, Dr.Math 
                    Uli

Date: 7/5/96 at 10:20:12
From: Doctor Darren
Subject: Re: Natural Number Start with 0 or 1?

When I first learned about natural numbers, I was told to think of
them as anything you could use to fill in the blank of the following
sentence: I have ____ bowls of ice cream (or pieces of cake, or piles
of dirt, etc.).

If you think of it this way, it is easy to see that only integers
count, and also that only positive numbers count as natural.

Furthermore, it is possible to have no ice cream, so zero must be
a natural number.

I hope this helps!

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

Date: 2/13/98 at 2:36:23
Subject: Re: Natural Number Start with 0 or 1?

I feel compelled to point out here that there's not solid agreement in the
mathematical community about whether zero is a natural number or not.  Some
say it is, some say it isn't.  Here are a few interesting discussions on
the topic, from the math-history-list:

http://mathforum.org/kb/message.jspa?messageID=1379424   
http://mathforum.org/kb/message.jspa?messageID=1379463   
http://mathforum.org/kb/message.jspa?messageID=1379474   

Several of the participants are well-respected mathematicians and math
historians.

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