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Math Help - Limits

  1. #1
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    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?
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  2. #2
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    Re: Limits

    Quote Originally Posted by Kristen111111111111111111 View Post
    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\}~?
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  3. #3
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    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
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