User blog comment:Rgetar/Number distinction/@comment-31837178-20171209160848/@comment-32213734-20171210233638

I thought so too (about difference between 3/6 and 5/10 etc). I was thinking about the concept of equality: it is usually understood that equality is equals sign and two objects to the left and to the right of it (X = Y), and this means roughly that X is the same thing as Y. But if X is the same thing as Y, we can write this as X = X, so, equality is tautology and something redundant. Why X = X, not just X? Or X = X = X? So, I think, equality should not be seen as "X is absolutely the same thing as Y". Indeed, 2 + 2 = 4, and is 2 + 2 absolutely the same thing as 4? No. 2 + 2 is expression, and 4 is number. I was thinking about "non-commutative" equality, but I did not come up with anything specific.