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Prove that if $x > 0$ and $x_n$ is a sequence with $\lim\limits_{n \to \infty} x_n = x$, then there is a real number $N$ s.t. whenever $n > N$, $x_n > 0$.

This is a homework question and I'm not really sure what methods I should use to prove this, can I get a push in the right direction? I am not expecting a flat out answer as it is a homework problem, but I am stumped!

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    @MattNashra: Well in terms of $\epsilon$s and $\delta$s, what does $\displaystyle\lim_{n \to \infty} x_n = x$, mean exactly?2011-10-31

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It's not necessary true: consider $x_n = -1/n$. Though it would be true if $x>0$.

Hint: consider the interval $(x-\epsilon,x+\epsilon)$ for $\epsilon = x/2$. Recall the definition of $\lim\limits_{n\to\infty}x_n=x$ in $N$-$\epsilon$ terms.