1. ## increasing sequence

Let A be a subset of R that is bounded above and let $u= sup A$ . Prove that there is an increasing sequence $a_n$ with $a_n \in A , \forall \ n \in N$ SUCH THAT $a_n \to u$

2. Originally Posted by flower3
Let A be a subset of R that is bounded above and let $u= sup A$ . Prove that there is an increasing sequence $a_n$ with $a_n \in A , \forall \ n \in N$ SUCH THAT $a_n \to u$
As written that is a false statement.
Let $A=[0,1]\cup\{2\}$.

It is true if we know that $u \notin A$.