Is Zero a Number?

Date: 07/05/2003 at 15:37:20
From: Joe
Subject: Zero and infinity

If infinity is not a number, then is zero really a number?  I see that 
it is not recognized as a real number but as a whole number, integer, 
etc. It seems as though zero has been accepted as a number and 
infinity has been accepted as a concept. This question stems from an 
argument about 1/0 = infinity.

Date: 07/05/2003 at 20:27:30
From: Doctor Jaffee
Subject: Re: Zero and infinity

Hi Joe,

Zero is a number; in fact, it is a real number.  It is on the number 
line right between 1 and -1. You can add, subtract, and multiply with 
0 and get real answers. You can divide numbers into zero and get a 
real answer, zero.

You can't say anything like that about infinity.  It is not on the 
number line and you can't do computations with it.

Now, consider 1/0. You know that 1/1 =1, 1/0.1 = 10, 1/0.01 = 100,
1/0.001 = 1000, etc... Pick a power of 10 as large as you want and I 
can find a number larger than 0 that I can divide into 1 and get your 
number as a result.

In other words, as we divide numbers into 1 and those numbers get 
closer and closer to 0, the quotient gets larger and larger with no 
boundary. We conclude then, that 1/0 = infinity.

For more about dividing by zero, see the Dr. Math FAQ:

   Dividing by Zero
   http://mathforum.org/dr.math/faq/faq.divideby0.html 

I hope this explanation helps.  Write back if you want to discuss the 
problem any more or if you have other questions.

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