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Please provide all work necessary for the entire question (a-c) in order to receive a thumbs up. Determine, with proof, that with the usual metric

Please provide all work necessary for the entire question (a-c) in order to receive a thumbs up.

Determine, with proof, that with the usual metric d(a, y) = (x - y| on R, a) Z is closed, b) [-1, 1) is neither open nor closed, and c) the transcendental numbers are neither open nor closed

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