# accumulation points or limits points

• October 26th 2010, 08:28 PM
alii
accumulation points or limits points
hello i am a new member and i expecting ur help

What is the set of accumulation points of the irrational numbers?
Give an example of abounded set of real number with exactly three accumulation points?
Let A subset of R A R and let x in R show that x is an accumulation point of A if and only if there exists of a sequence of distinct points in A that converge to x?
• October 27th 2010, 03:20 AM
tonio
Quote:

Originally Posted by alii
hello i am a new member and i expecting ur help

What is the set of accumulation points of the irrational numbers?
Give an example of abounded set of real number with exactly three accumulation points?
Let A subset of R A R and let x in R show that x is an accumulation point of A if and only if there exists of a sequence of distinct points in A that converge to x?

What is the definition of 'limit point"? What have you done? The set of limit points of the rationals (within the reals and the

usual topology) is a rather well known set which becomes pretty clear when one knows the definitions...

What happens with the set $S:= \left\{\frac{(-1)^nn}{n+1}\,,\,\frac{1}{n}\right\}\limits_{n=1}^\ infty\subset\mathbb{R}$ , with the inherited topology from the usual one?

Tonio