Is it strange that you can't divide by zero?

It may seem strange at first blush, but there's a pretty good reason why division by 0 isn't defined: if it were, we'd get an inconsistency. You can find many discussions of this point with a bit of googling, but the idea is simple. Suppose x = y/z. Then we must have

y = x*z

That means that if y = 2, for example, and z = 0, we must have

2 = x*0

But if we multiply a number by 0, we get 0. That's part of what it is to be 0. So no matter what x we pick, we get x*0 = 0, not x*0 = 2.

Is it still strange that we can't divide by 2? If by "strange" you mean "feels peculiar," then it's strange from at least some peoples' point of view. But this sense of "strange" isn't a very good guide to the truth.

On the other hand, if by "strange" you mean "paradoxical" or something like that, it's not strange at all. On the contrary: we get paradox (or worse: outright contradiction) if we insist that division by zero is defined.

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