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6:05 AM
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How about this question -
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Q: Is the set $\{(x,y)| x^2+y^2 = \frac{1}{n^2}, n \in \Bbb{N}, x\in \Bbb{Q}$ or $y \in \Bbb{Q}\}$ countable?

BAYMAXI was thinking about the set $\{(x,y)| x^2+y^2 = \frac{1}{n^2}, n \in \Bbb{N}, x\in \Bbb{Q}$ or $y \in \Bbb{Q}\}$ Certainly, this set is non-empty as I can find a pair $(\frac{1}{n^2},0)$ or like $(\frac{1}{2n^2},\frac{1}{2n^2})$ or in a more genral sense the points of the form $(\frac{a}{n^2},\...

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The comment of me
But can there be an uncountable subset within the main set? should that affect countability?
 

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