Let \(\rm S=\{(x, y) \lvert\, x^2+y^2=\frac{1}{n^2}\), where n ∈ ℕ and either x ∈ ℚ or y ∈ ℚ}.
Here ℚ is the set of rational numbers and ℕ is the set of positive integers. Which of the following is true?
1
S is a finite non-empty set
2
S is countable
3
S is uncountable
4
S is empty