Question

what does zero over zero represent?

Answer 1

it represents an indeterminate form. It shows up in the Calculus sometimes whem evaluating limits, for example, what sin(x)/x approaches as a limit as x approaches 0.
If you plug 0 into the expression and try to evaluate, you get 0/0, but the limit is 1.

Answer 2

If 0/0 is something, then something times 0 is zero, so something is any number which is not very useful.

Dividing anything by zero is definitely a bad idea in normal arithmetic.

Answer 3

1. anything divided by zero is undefined.
2. zero divided by anything equals zero

Rule 1 trumps rule 2, so 0/0 is actually undefined. As abtrehearn mentions, you see 0/0 a lot in problems of limits, where you are looking for the value of something infinitely close to zero, but not quite.

Answer 4

How about 0^0?

Answer 5

0^0 is usually treated as undefined / indeterminate in calculus, although it is treated as 1 in some fields, like combinatorics.