You need to learn a bit of mathematics here before making statements like that. For example, I can easily write what you call "0 times infinity" as "0 times 1/0". This means that what I have as "0 times infinity" is equal to 0/0. In mathematics, this is undefined! It totally depends on that kind of expression one is using to arrive at such a thing. If I have, for example sin(x)/x, where x approaches 0, then do you think I have 0 when x=0?
When arguing something based on mathematics, one truly needs to understand the mathematical rules. There are HUGE areas of mathematics that deal with the handling of "infinities". One only needs to take a class in complex algebra to realize this.