Tag: logically

Is it not logically wrong to make proofs in one field of mathematics, by using tools belonging to another one, since they start from different axioms?

It is as long as one does not prove the existence of an isomorphism (which between algebra and geometry is provable). If one postulates the continuity of real numbers and the continuity of points on a line, it can be shown that there is a one-to-one correspondence between numbers and points and t...