Math Help - Limits

1. Limits

I know how to prove by using the definition , if a sequence {an} is increasing and bounded above then Limit of {an} when n goes to infinity = sup{an|n belongs to positive integers} .

But how can I deduce, if a sequence {an} is decreasing and bounded below then Limit of {an} when n goes to infinity = inf{an|n belongs to positive integers} from the above proved theorem ?

I have proved those 2 by using the definition only. But I have a problem in deducing the 2nd one by using the 1st theorem. Can somebody please help me with it?

2. Re: Limits

Originally Posted by Kristen111111111111111111
I know how to prove by using the definition , if a sequence {an} is increasing and bounded above then Limit of {an} when n goes to infinity = sup{an|n belongs to positive integers} .

But how can I deduce, if a sequence {an} is decreasing and bounded below then Limit of {an} when n goes to infinity = inf{an|n belongs to positive integers} from the above proved theorem ?

I have proved those 2 by using the definition only. But I have a problem in deducing the 2nd one by using the 1st theorem. Can somebody please help me with it?
If you know that a sequence $\{a_n\}$ is decreasing and bounded below then what can you say about $\{-a_n\}~?$

3. Re: Limits

Well thank you.. When sequence \{a_n\} is decreasing and bounded below then \{-a_n\} is increasing and bounded above.. Guess I can use this to derive what I want Thank you very much for your help