In addition to the object level mistake that gwern has pointed out, you've made a meta-level mistake.

I wasn't arguing for the usefulness of Euclidean or non-Euclidean geometry. I was trying to shorten the inferential distance. Euclidean axiomatic mathematics is some of the first axiomatic mathematics anyone is taught in school in the West. The OP might not have understand what it was that his theory was missing in reference to infinite sets, so I used an example I expected him to be more familiar with, in an effort to make my point clearer to him.

You may not think my particular point is interesting in a practical sense, but pointing that out is quite rude unless you really think that I'm unaware that the difference between Euclidean geometry and real world geometry does not always make a practical difference.

It's like asserting the difference between Newtonian and relativistic physics doesn't make a practical difference. I don't know how true that is, but saying something like that to Einstein or Hawking is just rude.