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## Homework Statement

The question asks to prove that if (t_n) is a convergent sequence and suppose that its limit is great than a number x. The prove that it exists a number N such that n>N => t_n>x

## The Attempt at a Solution

I tried to say that as (t_n) converge, (t_n - x) converges too.

And let lim(t_n - x) = k, for k in R (real).

Then for some e>0, there's a number N s.t. n>N => |(t_n-x)-k|< e

Take e=0, then |(t_n-x)-k|=0 => t_n-k = x,

since lim(t_n)>x then k must be positive => lim(t_n)>x.

can anyone tell me if i am going the wrong way??

I am afraid that my concept somewhere is wrong..

Thanks