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
