Show there exist a natural number n

[pinguhash]

Show there exist a natural number n...

1. Let {x_n} be a sequence of reals which converges to x > 0. Show that there is a natural number n₀ such that x_n > 0 for all n >= n₀ .

I tried this but cannot approach the answer.
Can anybody?

 

[lanedance]

what is the definition of convergence?

 

[pinguhash]

what is the definition of convergence?

The sequence (x_n) is said to converge to a real number
a.
if for all ε>0, there exists N in N such that |xn-a|<ε for all n≥N.

 

[lanedance]

ok so how about picking a useful ε>0...