1+1=2 and, discarding any mildly clever counter-examples that don't really matter (eg 1.4 + 1.4 = 2.8, which rounds to 3), I have a hard time imagining how the discrete quantity 1 could ever be added to the discrete quantity 1 to produce anything other than the discrete quantity 2.
Of course I'm not talking about the symbols themselves, the concepts they represent.
Now, it's my opinion that mathematical facts are more real than reality itself. That this universe and all possible univereses will rely on these types of facts. Obviously you can imagine universes with different physics from our own, different ways of dealing with space and time, and there may be certain clever ways of arranging space that make certain intuitions about quantities weird, but they aren't weird because the numbers work differently, they're weird because the numbers are put into a weird context.
So it would be my view that any reality cannot escape certain mathematical facts, it can only manipulate them into stragenesses, and so these mathematical facts are unchangable even in principle.
I know there are probably other views than that, and I may actually just be objectively wrong, so I guess my question is two-fold:
What are the names of these positions, and am I objectively wrong?