Recent content by matematiker

Now I am trying to prove the statement in the other direction: Let a,b,c be reals and let A be a set of real numbers. If c<b and there is an a in A such that a>c then b is the supremum of A. From the givens I know that: c<b There is an a in A such that a>c. What I need to prove is that...

That would mean b is not the least upper bound since c is smaller than b and greater or equal to any a in A which is a contradiction since by hypothesis b is the supremum of A. Awesome ! Thank you clamtrox !

Homework Statement Let A be a set of real numbers. If b is the supremum (least upper bound) of the set A then whenever c<b there exist an a in A such that a>c. Homework Equations The Attempt at a Solution I considered two cases. The first one when the supremum b is attained by...