What's the square root of William Lane Craig?

I heard the following quote in a debate to which one party was a philosopher and Christian apologist William Lane Craig (no link, he's easy enough to find if you're into that sort of thing):

Mathematicians recognize that the existence of an actually infinite number of things leads to self-contradictions. For example, what is infinity minus infinity? Mathematically, you get self-contradictory answers.

Assuming that Craig's premise ("Infinity minus infinity is undefined") is true, his argument is ridiculously wrong. To see this, replace his premise with another (true) one, and watch it lead to an absurd conclusion:

Mathematicians recognize that the existence of a number that represents null leads to self-contradictions. For example, what is zero divided by zero? Mathematically, you get self-contradictory answers.

Craig is confusing coherence with applicability. Yes, the division function is undefined for the pair (0,0); but this doesn't mean that "zero" is a self-contradictory concept. Similarly, the fact that the subtraction function is undefined for the pair (infinity,infinity) does not mean that the concept "infinity" is nonsensical. There doesn't exist a single relation defined for all possible things in the world, so when you're talking about relations, you need to remember to stick to their respective domains. If you don't think this is an important distinction, I have a puzzle for you. It's the title of this post.