Concept explainers
Prove that
(a) if x + y is irrational, then either x or y is irrational.
(b) if x is rational and y is irrational, then
(c) there exist irrational numbers x and y such that
(d) for every rational number z, there exist irrational numbers x and y suchthat
(e) for every rational number z and every irrational number x, there exists aunique irrational number y such that
(f ) for every positive irrational number x, there is a positive irrational numbery such that
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A Transition to Advanced Mathematics
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