# limit proof

• February 2nd 2011, 12:52 PM
mremwo
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:
$
\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!!
• February 2nd 2011, 01:02 PM
Plato
In the definition of sequence convergence use $\varepsilon = \dfrac{x}{2}>0$

Then get $-\dfrac{x}{2}.

Carry on.