Is infinity divided by infinity, 1 or infinity? ....?

Infinity divided by infinity is an example of

what is called an indeterminate form. What it

is depends on the context in which it arises,

typically in a limit situation. Some algebraic

manipulation is needed to eliminate the

indeterminate form.

It's like asking is apples divided by oranges 9 or 17.

Infinity is not a number, therefore the operation of division does not apply.

∞ is not a number, so your question is, strictly speaking, meaningless. Infinity comes into play when we are dealing with limits. The FORM ∞/∞ indeterminate, meaning we must use l'Hopital's rule or some other method to evaluate the limit, if it exists.

It's 1. It's the same concept as 10 / 10 or 100/100 as always one. Any number divided by itself is one.

( ∞ ) / ( ∞ ) is an indeterminate form...

http://www.math.fsu.edu/~bellenot/class/f99/cal1/i...