1. does not exist

2. indeterminate

3. undefined

what exactly do these terms mean, when do they apply and when is it appropriate to use them (concerning math of course)?

for example, if you had f(x) = 1/x, when x = 0 how would you describe it?

another question.

if f(x) = (x^2 - 2x - 3) / (x-3)

f(3) = 0/0 by direct substitution. however, if you factor the dividend it becomes

f(x) = (x-3)(x+1) / (x-3)

f(3) = 4

so which answer is right?

can an answer only ever be 0/0?

what would you call (using the three terms above if they apply) a 0/0 answer?

thanks