# Thread: Find Accumulation points and Isolation points of set X, Y, Z and W in R^2

1. ## Find Accumulation points and Isolation points of set X, Y, Z and W in R^2

1)
X={(2a,2b) | a,b integers}

2)
Y={(p,q) | p,q rational}

3)
Z={(1/n,m/n) | m,n integers, n not equal 0}

4)
W={(1/n+1/m,1) | m,n integers, m and n not equal 0}

Hope someone can help... very confused and struggling

2. ## Re: Find Accumulation points and Isolation points of set X, Y, Z and W in R^2

Do you know the definitions of "accumulation point" and "isolated point"?

Have you drawn a picture of these sets?

If you know the basic definitions (1) and (2), at least, should be easy.

3. ## Re: Find Accumulation points and Isolation points of set X, Y, Z and W in R^2

Hi HallsofIvy,

Thank you for your reply. I read alot of the definitions in text and online and I'm not too sure if I have understood correctly. So for the 1st question. The set X is a set of even numbers right? So is acc(X) a set of even numbers?

4. ## Re: Find Accumulation points and Isolation points of set X, Y, Z and W in R^2

no, the first set is a set of *pairs* of even numbers. like a(n infinite) page of "dots" spaced 2 apart.