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(1) x^2 < 1 => x < 1 so OK
(2) |x| < 1/x => x < 1/x or x < -1/x, then,
x < 1/x is possible only if x < 1, but it can be any number 0<x<1 and x < -1, so it does not tell us if |x| is < 1,

if we take x < -1/x, is possible if x <= -1 ... can't say.