In ZFC theory (fundamental maths), "A in B" means "there is a relation between A and B, and this relation is called 'in'". Replace 'in' by the correct math symb

In ZFC theory (fundamental maths), "A in B" means "there is a relation between A and B, and this relation is called 'in'". Replace 'in' by the correct math symbol or anything you want, it works the same. From this, we can define a new relation called "=" such as: for all x in A and for all y in B, x in B and y in A We don't care what A, B, x or y are. We don't care what "x in A" means. It's just logical statements that are useful, and we build the rest of maths upon it. For me "=" does not mean "equal", "equivalent", or anything. It means "there is a relation between 2 objects". For example: - in a programming language "a = 3" means that "a" is related to "3" - in a BNF grammar "rule := term term term" means that "rule" is related to "term term term" - in a math equation "y = x + 1" means there is a relation between "y" and "x + 1" - on some old calculator "A <- 1" means there is a relation between "A" and "1" In each of those domains, the relation is precisely defined. But it does not need to be the same relation (they are different math theories). Another example, "y = x + 1" could be interpreted as "there is a value for x for which I can replace x + 1 by y". You don't even have to care about what "x + 1" means.