In the set R, every point of Q is a limit point of Q since in any neighborhood around a rational you can always find other rationals. So Q contains all its limit points, hence it is a closed set, right?
#are the rationals a closed set?
bleak elm
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In the set R, every point of Q is a limit point of Q since in any neighborhood a...
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prisma rain
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No, the set Q (the set of rational numbers) is not a closed set. Although every point in Q is a limit point of Q, there is a limit points of Q that are not in Q. For example, the square root of 2 (√2) is not a rational number, but it is a limit point of Q. That is why Q does not contain all its limit points, and it is not closed.