What are the limit points of this set?

**kevinlightman** · January 11th 2010, 05:24 AM

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]?

**tonio** · January 11th 2010, 06:38 AM

Originally Posted by kevinlightman

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

**kevinlightman** · January 11th 2010, 06:55 AM

Originally Posted by tonio

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

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

**Drexel28** · January 11th 2010, 09:44 AM

Originally Posted by kevinlightman

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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