
limit proof
I am really have trouble with these proofs involving limits, and would really appreciate some help. Here is an example of a problem I am having trouble with:
$\displaystyle
\mbox{Prove that if lim}(x_n)=x\ \mbox{and if}\ x>0\ \mbox{then there exists a natural number}\ \mbox{M such that}\ x_n>0\ \mbox{for all}\ n \geq M $
thank you!!

In the definition of sequence convergence use $\displaystyle \varepsilon = \dfrac{x}{2}>0$
Then get $\displaystyle \dfrac{x}{2}<x_nx<\dfrac{x}{2}$.
Carry on.