First of all either learn to use LaTeX or do not use special fonts.
Suppose that .
Using and the definition of sequence convergence prove that there is a p.i. N such that .
Now let .
You are done if you fill in the details.
Suppose that sn is a sequence of positive numbers converging to a positive limit L. Show that there is a c > 0 such that sn > c for all n.
I can do this for sn < c using the limit definition, but I don't know how to show this.
First of all either learn to use LaTeX or do not use special fonts.
Suppose that .
Using and the definition of sequence convergence prove that there is a p.i. N such that .
Now let .
You are done if you fill in the details.