Thread: closure , metric space

Hello,
i have a exam coming tomorrow and i need some hints or the solution for this problem. This is a practice problem

thank you in advance

Let A ⊆ R be a subset of non-empty and increased. Show that the point x = sup A ∈ R (which exists by the axiom of Dedekind) is adherent(closure) to A.

Originally Posted by donsmith

Hello,
i have a exam coming tomorrow and i need some hints or the solution for this problem. This is a practice problem

thank you in advance

Let A ⊆ R be a subset of non-empty and increased. Show that the point x = sup A ∈ R (which exists by the axiom of Dedekind) is adherent(closure) to A.

What does of non-empty and increased mean?

not empty and bounded