Difference between A = {(x,y) ∈ (R\Z)²| |x|<2, |y| ≤ 2} and A = {(x,y) ∈ R²\Z² | |x|<2, |y| ≤ 2}

[Ingeniosus01]

Respect, I have a problem with this, I am aware that no one is there to do the assignment for me, this is not homework but an exam assignment from the last term, but the problem is that I don't even know how to approach the problem.
What is the difference between these two sets and how would they look when drawn or described.
A = {(x,y) ∈ (R\Z)²| |x|<2, |y| ≤ 2} and
A = {(x,y) ∈ R²\Z² | |x|<2, |y| ≤ 2}

P.S. The assignment asks me to determine the interior point of the set, the adherent point, the accumulation point, the edge point, and the isolated point.
Are they have all the same, what is the main difference?

Thanks in advance!

 

[Dr.Peterson]

Respect, I have a problem with this, I am aware that no one is there to do the assignment for me, this is not homework but an exam assignment from the last term, but the problem is that I don't even know how to approach the problem.
What is the difference between these two sets and how would they look when drawn or described.
A = {(x,y) ∈ (R\Z)²| |x|<2, |y| ≤ 2} and
A = {(x,y) ∈ R²\Z² | |x|<2, |y| ≤ 2}

P.S. The assignment asks me to determine the interior point of the set, the adherent point, the accumulation point, the edge point, and the isolated point.
Are they have all the same, what is the main difference?

Thanks in advance!

The real question here is just this: What are the sets (R\Z)² and R²\Z²?

If you need help on that, think about which of these pairs are in each:

• (1, 2)
• (1, 0.2)
• (0.1, 2)
• (0.1, 0.2)

Please tell us your understanding of this, and either you'll see the answer to your question, or we'll be able to correct a misunderstanding.