Where can I find the mathematical proof of this?

Question

It says something like this:
"Numbuer ONE exists and is unique".

Thanks.

I mean NUMBER!! Sorry.

Answer 1

One, by definition, is the cardinal number of all sets whose elements can be put into 1-1 corespondence with the elements of this set: { N}. It exists because we define it to exist with the property that 1 x n = n for all real numbers n.

Assume that 1 is not unique so that there is another number y
with the property that y x n = n for all real numbers n.

Then by transitive property of equality

y x n = 1 x n since both equal n. But for nonzero n

y = 1 by cancelling the common factor n.

But this contradicts our assumption that 1 is not unique since we have now shown that any number y such that y x n = n is in fact the unique number 1.

Answer 2

Wao!!!!!!