It is a very intuitive question, actually is very trivial... I have to show that $S\,'\!\subset \overline{S}$.
Using the definition of limit point ,we have :
$\forall \epsilon>0, \big(]x- \epsilon ,x+\epsilon[\;\cap\; S\big)\setminus \{x\} \neq \emptyset$
But, also, the definition of closure is
$\forall \epsilon>0, \big(] x- \epsilon ,x+\epsilon [\;\cap\; S\big) \neq\emptyset$
So, every limit point is also a closure point. Is that right?
How could I write it? That is being my problem: I know it, it's quite obvious by the definition, but I can't write it in a proper way...
I say that limit point is a subset of closure because "it is the closure minus a point"?
(I'm sorry my stupidity...)