Infinity is not a cheat

I was watching What Happened Before the Big Bang? on the Science Channel. There are some clips on YouTube from last year's BBC Horizon version, such as here. At about a third of the way, and at the end of the YouTube clip, it says:

Eventually that space will become infinitely small, and in mathematics, invoking infinity is the same as giving up, or cheating.

I don't know how anyone could say anything so silly. Studying infinities has been a central object of mathematics for centuries.