I was a little surprised at the teacher's response. Wittgenstein's argument is fairly firmly in Philosophy of Mathematics and not something taught in most undergraduate maths degrees, whereas the various constructions of infinity (of which this is just one) are pretty standard stuff. In fact, if anything, I'd expect a school maths teacher to assume that the existence of infinity was something proved by Cantor's diagonal argument (*ahem* maybe another time!) rather than proclaiming point-blank that there was no such thing.