Thread: real analysis test question

Suppose that lim s(sub n) =s, with s >0. Prove that there exists an N in R (real numbers) such that s(sub n) >0 for all n in N.

Hello,

Originally Posted by trojanlaxx223

Suppose that lim s(sub n) =s, with s >0. Prove that there exists an N in R (real numbers) such that s(sub n) >0 for all n in N.

means that :


Now take such that is positive. You can always find one, such as

From the inequality , we can say that
Since we defined such that , it's easy to conclude.