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..