Fraction with Zero question

This is for the *genuises*. when posed with the problem, "what is the answer to 0/0?" i have come across three different solutions and im not sure which is correct:

1. since any fraction with 0 as the denominator cannot be solved, then the answer is "undefined"

2. since any fraction with 0 as the numerator is zero, then the answer is "zero"

3. finally, since any fraction in which the denominator and the numerator have the same numerical value is equal to one, the answer must be "one"


so which one is correct?

>>16
No, they're... They're doing it wrong.
0/0 is undefined, and is part of a group of indeterminate forms (such as 0^0, inf/inf, etc.). 0/0 does not equal DNE. DNE is what you get as the result of taking a limit that doesn't actually exist.
Example:
The limit of 1/x as x approaches 0. Looking at the graph of 1/x, you can see that coming from the left, 1/x approaches -inf. Coming from the right, it approaches inf. Because there is a disparity where the two meet (i.e. it is both infinity and negative infinity), the limit is said not to exist.
You can't use NaN or DNE in any sort of equation; they're just what you get when you've screwed up somewhere.