Infinity Times Zero is Not Zero

The problem is that the laws of addition and multiplication you are using hold for natural numbers, but infinity is not a natural number, so these laws do not apply. If they did, you could use a similar argument that multiplying anything by infinity, no matter how small, gives infinity, thus ∞×0=∞. More sophisticated arguments can also be made, like ∞×0=limx→∞(x×1/x)=1. Clearly all these different values for ∞×0 mean that ∞ cannot be treated like other numbers. In order to ...