If A is a nonempty subset of R Proof that bsupA We show two

If A is a nonempty subset of R. Proof that b=supA.

We show two things:

1- b is is an upper bound for A

2- b is a least upper bound.

Am I right?

Solution

sup A is by definition the least upper bound.

1. You prove that b is upper bound of A

2. Now in second step you can assume another element, a<b is also an upper bound of A

And then arrive at an contradiction hence provign b is least upper bound.