Infinity * Zero = Any Number ARGUE HERE

[EI_Tizzy]

Well, I don't know if anyone in here is in Calculus, but you can have infinity x 0 = any number... it just depends how you arrive at infinity and zero. Also, you have to assume you CAN go out to infinity.

For instance, take the limit of x sin(1/x) as x goes to infinity. The "x" term will approach infinity (obviously), and the "sin(1/x)" term approaches 0. Yet, as we can see on a graphing calculator, the ends of this equation clearly go to 1. So in this case, infinity x 0 = 1.

In another example, take the limit of x ln(x) as x goes to 0. The "x" term reaches 0 and the "ln(x) term reaches -infinity. Using l'Hopital's Rule with (ln(x))/(1/x), the limit is now (1/x)/-(1/x^2). Multiply top and bottom by x^2 and now the answer is the limit of -x as x goes to 0, which is 0. Here, infinity (or rather, -infinity) x 0 = 0.

It all depends how the numbers are reached...