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