Question: I was thinking the other day when i was in math class that when you divide 1 by say n you'll get 1/n. As the value of n increases the smaller the number you get. So if you divide 1/infinity would that equal zero? And if that is true then would 1/0=infinity be true also?

Hi Evan,

Your observation that

As the value of n increases the closer 1/n gets to zero.

is correct and is a very important idea but I don't like writing 1/infinity. The arithmetic operations apply to numbers and infinity is not a number so I don't like the idea of trying to divide by something that is not a number. Nevertheless I would like a more mathematical way to say

As the value of n increases the closer 1/n gets to zero.

To do this mathematicians use the idea of a limit, which is the fundamental concept of calculus, and say that the limit of 1/n as n approaches infinity is zero, and write this statement

If you apply the same idea to try to evaluate 1/0, that is you ask

As the value of n gets close to zero what happens to the value of 1/n?

I am thinking of n as a positive number. If you try this you realize that as n gets close to zero, 1/n gets larger and larger and doesn't approach any finite value so I might say

The limit of 1/n as n approaches zero is infinity.

or what I prefer to say is that

The limit of 1/n as n approaches zero does not exist.

As n approaches zero, 1/n just doesn't approach any numeric value.

You can find another approach to attempting to evaluate 1/0 in the answer to a previous question.

Penny