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Hi so my question is asking to prove if 1/x is bounded when x belongs to the interval [1,infinty).This is the answer I came up with: Let M = 1 then (1 ≤ x) = (|1| ≤ x) = (-x ≤ 1 ≤ x) = (-x/x ≤ 1/x ≤ x/x) = (-1 ≤ 1/x ≤ 1) = (|1/x| ≤ 1) for all values of x on the interval for [1,infinty).
This is my proof, if the proof is wrong then tell me what I did wrong, also the wording or the order of the proof might be weird so please help me with that. I am trying to learn real analysis. Thank you.
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