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Math Help - What are the limit points of this set?

  1. #1
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    What are the limit points of this set?

    What are the limit points of the set containing x^n such that n is in the positive natural numbers for each a that is a member of the inteval [-1,1]?
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  2. #2
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    Quote Originally Posted by kevinlightman View Post
    What are the limit points of the set containing x^n such that n is in the positive natural numbers for each a that is a member of the inteval [-1,1]?


    x^n=1 \Longleftrightarrow x=1\,\,\,or\,\,\,x=-1\,\,and\,\,n\,\,even\,,\,\,x^n=-1\,\,if\,\,x=-1\,\,and n\,\,odd\,,\,\,and\,\,\,x^n\rightarrow 0\,\,\,if\,\,\,|x|<1

    Now prove the above and you get your answer.

    Tonio
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  3. #3
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    Quote Originally Posted by tonio View Post
    x^n=1 \Longleftrightarrow x=1\,\,\,or\,\,\,x=-1\,\,and\,\,n\,\,even\,,\,\,x^n=-1\,\,if\,\,x=-1\,\,and n\,\,odd\,,\,\,and\,\,\,x^n\rightarrow 0\,\,\,if\,\,\,|x|<1

    Now prove the above and you get your answer.

    Tonio
    I have already done this, it is more the concept of limit points I don't understand, I believe 0 to be one for every value not equal to -1 1 or 1 but I can't see what the others would be
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by kevinlightman View Post
    I have already done this, it is more the concept of limit points I don't understand, I believe 0 to be one for every value not equal to -1 1 or 1 but I can't see what the others would be
    Tell me, what is a limit point? Why do you think that 0 is a limit point of this set?
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