When I imagined a way to demonstrate the theorem I did many attempts and I chose the one that sounded the most natural (because saying that the more you go in dept in Mathematics the more cool it becames sounded natural to me), but if you have an alternative solution please tell me! It was the purpose of the article to make all of you think and imagine!
Anyway I know that Mathematical topics are countable but I though that if I would have stated that there are, let's say, 10 topics in mathematics, someone else could argue that there 11 topics because he counted them in another manner; so I preferred to keep it general, without numbers.
In the end, even if all would have accepted that there are 10 topics in mathematics what would you do with that? Basically you have to demonstrate that C(Tn) > 0 ∀ n of N. But I don't see any advantage by knowing the exact amount of topics...
But, as I have already said, if you have another answer I happy to hear that!