Course: Intro to Real Analysis
I'm trying to prove , where and are bounded sequences. There are only theorems for limit superior in our chapter, so I was wondering if I could somehow manipulate the following theorem:
Let be a bounded sequence. Then the following properties hold:
(a) For every there exists a natural number such that implies that .
(b) For every and for every there exists an integer such that .
Can I say the following?
For every there exists a natural number such that implies that .
For every and for every there exists an integer such that .