> There is a big difference between “infinity doesn’t exist” and “infinity doesn’t exist physically”.

Is there? I think one could make a decent case for "nothing exists which doesn't exist physically[1]".

[1] https://plato.stanford.edu/entries/physicalism/

EDIT: you could even probably claim "nothing exists which isn't physically measureable" which may or may not be a stronger claim depending on your point of view.

EDIT AGAIN: rate limited by this dogshit website :D but I'll respond to this comment here:

> Which is exactly why I mentioned rejection of zero, negative numbers, etc. You can reject them, but doing so just throws away useful tools without gaining anything in return.

Yeah! I fully agree. I can see no obvious benefit to rejecting these powerful tools. However, important discoveries often happen in non-obvious directions, and exploring unexplored territory is generally worthwhile. So the fact that it doesn't seem immediately useful doesn't mean it's not worth trying!