What If There Was No Zero?

Date: 10/21/2003 at 07:18:33
From: Melissa
Subject: the importance of zero

If the zero is so important, why did it take so long to be discovered?
   Why did some civilisations just not need to have a zero?  And also,
could you please give me some examples of what we can now do in maths
that we wouldn't be able to do if we didn't have the zero?  If we had
never discovered the zero, what sort of maths wouldn't we be able to
do?  Where would maths stop?

I cannot imagine maths without zero!  I had to do a project on the
history of the zero.... and as I was presenting it, I was really
trying to find an answer to those questions, but I never did!

Date: 10/21/2003 at 12:43:30
From: Doctor Peterson
Subject: Re: the importance of zero

Hi, Melissa.

I think that without the concept of zero (and negative numbers, which 
go with it, and may even have led to its full acceptance), algebra 
would have stagnated at about the stage it reached around 800 AD.  The 
problem is that many things we do in algebra either require zero in 
order to be expressed neatly (such as inverse operations), or would 
have to be done in several separate cases according to whether some 
variable or coefficient was positive, negative, or zero.  Including 
these numbers unifies everything and makes it possible to do much 
more in a single solution. Without them, much of algebra, calculus, 
and beyond would have remained too difficult to learn, apply, and 
build on.

Yet until you get to algebra, there is really no need for zero!  It 
helps as a digit in our number system, but earlier number systems did 
fine without it, because they were not used for anything but counting 
and measuring real objects, using positive numbers.  It is only when 
you want to extend the reach of numbers, and start using variables, 
that you find zero and negative numbers necessary.

Here are a few discussions of the history of zero from our site (and 
one favorite link) that will help answer your questions:

  A History of Zero
    http://www-history.mcs.st-and.ac.uk/HistTopics/Zero.html 

  Why is Zero Not a Natural Number?
    http://mathforum.org/library/drmath/view/57186.html 

  Purpose of Zero
    http://mathforum.org/library/drmath/view/57051.html 

  History of Zero and Place Value
    http://mathforum.org/library/drmath/view/52566.html 

  Year 0
    http://mathforum.org/library/drmath/view/52475.html 

  Zero for Children
    http://mathforum.org/library/drmath/view/58763.html 

  Practical Applications of Negative Numbers
    http://mathforum.org/library/drmath/view/61468.html 

  Negative Number History
    http://mathforum.org/library/drmath/view/52593.html 

I found these just by searching our site for "history zero" and
"history negative".

If you have any questions that are not answered there, feel free to 
write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/