What is the Definition of Zero? Who Invented the Symbol?

Date: 9 Jan 1995 12:18:50 -0500
From: David Chen
Subject: Ask a question

Hi, Dr. Math
        I am a student from Monta Vista's Internet class and I am here to 
ask you a question about math. I really wish that you can help me answer 
the questions. My question is: What is the definition of zero, and who 
invented or introduced the symbol to represent the zero?  

Thanks in advance.
                           Sincerely,  David Chen

Date: 10 Jan 1995 03:48:57 -0500
From: Dr. Sydney
Subject: Re: Ask a question

Dear David, 

        Hello!  I'm glad you wrote to Dr. Math.  The concept of zero is
surprisingly deep, and it took human thinkers quite a long time to come up
with the notion of zero.  In fact, though mathematicians began thinking
about the concept of zero in 2000-1800 B.C.E., it was not until about 200-300
B.C.E. that the Babylonians began using a symbol that would evolve into 
what we today know as zero.  

        It turns out that mathematicians first thought of zero in the
context of writing numbers down -- zero was first a placeholder.  Before
mathematicians understood the notion of zero, there was much ambiguity 
about written numbers.  For instance, if the symbol for 5 was written down, 
there was no way to tell what number was being expressed -- was it 5? 
Or, 50?  Or, 5,000,000?  Thus, zero was introduced as a placeholder to avoid 
these ambiguities.

        In India, the concepts of 0 as a placeholder and 0 as a number were
associated with one another much earlier than in Babylon.  It is from the
Indians that we get our present-day symbol for 0.

        I don't have an exact definition for 0 here with me at home.  I can
tell you this:  when working with sets or groups of elements under some
defined operation of addition, the "zero element" is defined as the element,
let's call it z, such that a + z = a for all a in the set or group.  So, one
definition you could use for 0 is that 0 + x = x for all real numbers x.
Alternatively, you might define 0 as the number in between the positive and
negative numbers.  Or, maybe you could define 0 as lacking quantity (that's
what the dictionary says!)  What do you think about these different
definitions?  If you are looking for a different definition, write us back,
and we'll try to find a better one.  

        I hope this helps.  Write back if you have any questions.

--Sydney, Dr. "whoa" math