To 40, I don't know, it's my way of seeing it. A part of me is right and a part of you is right. The proof I made isn't really.. a proof, it's a way to show that..
0 * x does not equal 3 [zero times x (a number) always equal zero]
And when you or a calculator try to find it, there's no number that can find any number that can get the answer if you multiply a number by zero. You'll just.. have no answer to that, which can be put as "Undefined" or "Does Not Exist"
I may not be "teh" best at math explanations or being "teh" Win either.
Here's another explanation (or another way to be flamed at, depends) a bit more English oriented but, your call.
Anon Way
Take 3/0 as the example... It's like saying "You have 3 people but I want to split you guys into groups of eh.. GTFO ALL OF YOU" And it's like nothing happens, and they all go back to 4chan. Yay...
Math Way (Calculus)
lim [f(x)-f(c)]/(x-c)
x->c
Given
f(x) = x^2 - 1
c = 2
If you plug in the equation as it is, without simplifying, you'd end up as:
x^2-4/(x-2)
On the denominator (x-2), you attempt to plug in c = 2, 2-2 = 0 and if your numerator is any number but zero... It will turn out "Undefined" (In this case, it's 4/0) And the purpose of finding limits is to know what point y is at when x APPROACHES that number. If this problem can't factor out, then it is truly "Undefined", but in this case, it can be factored.
End up simplified as:
(x + 2)(x - 2) / (x - 2)
The (x - 2)'s cancel out...
and 2 + 2 = 4
***Note : This math section shows a bit more than needed with the 'divide by zero' thing.