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Let $A$ a subset of $R$. Then $A$ is called dense if and only if every point $x\in R$ is a limit of some sequences of elements of $A$.

The if part is by definition, I don't know how prove the only if part.

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The definition goes both ways. There is nothing to prove until you have an $A$. –  Ross Millikan Nov 17 '12 at 19:03
    
Sorry, but my teacher send me this exercise. I think that must be more difficult that this answer. –  Rafael Jiménez Guerra Nov 17 '12 at 19:25
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What you gave is a definition. There is nothing to prove. Perhaps the next part of the exercise is missing? Or you want to show that this definition is equivalent to another one, which you didn't write here? –  Petr Pudlák Nov 17 '12 at 20:33
    
Definitions are always "if and only if" statements, even if we are sometimes careless and don't state them that way. $n$ is even if and only if it's a multiple of 2. $x$ is positive if and only if it's greater than zero. –  Gerry Myerson Nov 17 '12 at 21:47
    
A question, I know it don't relation with the Problem of dense but: $\sum$$\frac{n+k}{n^2+k}$ for k=1 to n. The limit is $\frac{3}{2}$ but, Why? –  Rafael Jiménez Guerra Nov 18 '12 at 20:34
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