What if greatest lower bound equals the least upper bound in a set? If A is a non empty bounded subset of R, and the g.l.b for A equals the l.u.b for A , what can be said about A?
My answer: A contains precisely one point. Am I right?
I am asked to find an example of a countable bounded subset A of R whose g.l.b and l.u.b. are both in R-A.
I know some countable subsets of R, they are set of positive integers, integers, natural numbers, rationals. But they are not bounded. If I take any open or closed interval in R, they are bounded but not countable. So, any hint or idea is welcomed.
Thanks in advance.

You're right. In fact, it doesn't matter that they're the greatest lower bound and least upper bound. Using the definition of a lower bound $L$ and an upper bound $U$:
$L \leq x$ for all $x \in A$
$U \geq x$ for all $x \in A$
So if $L = U$, then $L \leq x \leq L$ for all $x \in A$, which means that $x = L = U$ for all $x \in A$.
