Math Help - Accumulation points, dense set

1. Accumulation points, dense set

Let S be contained in $\mathbb{R}$ and let A be the set of accumulation points of S. Prove S is dense in $
\mathbb{R}$
iff. A= $
\mathbb{R}$

2. Originally Posted by pirouette
Let S be contained in $\mathbb{R}$ and let A be the set of accumulation points of S. Prove S is dense in $
\mathbb{R}$
iff. A= $
\mathbb{R}$
What is your definition of dense? Is it that for each ball in the reals, it contains a point of S?

If so then suppose that S is dense. Let $x \in \mathbb{R}$, then for each open set around x, it contains an element of S. Hence $x \in A$. As x was arbitrary, we have that $A=\mathbb{R}$.

Similarly the other way round.