Given S is a subset of R
Suppose S' (set of all accumulation points in S) = emptyset
Prove S is countable.
I think I am supposed to use the Bolzano-Weierstrass Theorem but I can't figure out how to apply it.
Bolzano-Weierstrass Theorem : Every bounded infinte set in R has an accumulation point.
We have another basic fact for countable set: the union of countable ...
The Bolzano-Weierstrass Theorem is applied to proving a set is countable. The proof is concise.