# What are the limit points of this set?

• January 11th 2010, 06:24 AM
kevinlightman
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]?
• January 11th 2010, 07:38 AM
tonio
Quote:

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]?

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

Tonio
• January 11th 2010, 07:55 AM
kevinlightman
Quote:

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

Tell me, what is a limit point? Why do you think that $0$ is a limit point of this set?