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Your example is wrong even in our universe lol. In the trivial ring (https://en.m.wikipedia.org/wiki/Zero_ring ), 0=1 is true.
What you are probably imagining when talking about 0 and 1 are their representatives in the “integer ring” or maybe the ring of real numbers. Both are simply definitions made by humans and in no way universal truths.
How many years have you studied mathematics? If you really believe that, it can’t be more than 2 after high-school.
Edit: better question: Can you define “equivalence relation”? I don’t want you to be creative, I want the standard definition you come across in any foundations class.
