I interpreted that phrase as small-but-not-infinitessimally-small (infinitessimally small might be 1 particle per billion light years of space, while small might be 1 particle per 10 light years, or something). Of course, he probably could have meant non-zero.
It's funny; you've made me realize that when I use "finite", I'm always thinking out the other direction on the number line. To me, vernacular "finite" means "Really big, but not infinite". It implies a stop sign on that big 'ol highway to infinity and beyond.
However, finite here is used as a synonym for quantifiable, and that definitely sounds ok to my ear.
WTF? How can you say zero is not a number? In some cases it's not considered a part of the set of natural numbers but it has always been a member of the integers, the rational and of course the real numbers.
Sheesh. To say zero is not a number is completely inaccurate. It even says so on wikipedia so it must be true!