argv wrote:And it makes sense to me: as the divisor approaches zero, the result approaches infinity, so it follows that a divisor of zero ought to result in infinity.

Nothing makes sense when division by zero is involved.

Keep in mind that division is the inverse operation of multiplication. That is to say, if you have X × Y = Z, then you also have Z ÷ Y = X. Based on that, if some random number, let's say 12, is divided by zero and gives you infinity, then that means that infinity multiplied by zero gives you 12. Do you see the problem?

Even better: X ÷ X = 1. This is true for every number. So what is X = 0? Shouldn't you get 0 ÷ 0 = 1? But wait, 0 ÷ X = 0; this also is true for any number. So 0 ÷ 0 = 0? But it's also equal to 1 and to infinity!

Therefore, if X ÷ 0 is legal, then 0 = 1 = infinity. Good luck getting the rest of your maths to still work after that.