Comment by perforator

Your statements such as

> We know that there’s only one 1 in the rational numbers, then it must be the same 1 object as the 1 in the integers. > The statement “3/3 is in Z” is true.

make it sound very trivial while in reality it is not. I do not quite understand your example with R^3 but the defined applies equally to your statements. There are many ways to define and think about the objects you mentioned -- there is not one single truth. Unless you are a devoted platonist, in which case, it's still like your opinion, man.