Hi, Prove or disprove that a. sum of two distinct irrational numbers is irrational. b. Product of two distinct irrational numbers is irrational
Last edited by mr fantastic; August 28th 2011 at 05:41 AM. Reason: Re-titled.
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Originally Posted by MathsNewbie0811 Hi, Prove or disprove that a. sum of two distinct irrational numbers is irrational. b. Product of two distinct irrational numbers is irrational a) Use a simple counterexample, like b) Use a simple counterexample, like ...
Originally Posted by Prove It a) Use a simple counterexample, like b) Use a simple counterexample, like ... I suspect the OP's use of the word 'distinct' implies 'different'. @OP: and provide the necessary counter example for disproving the statements in both (a) and (b).
Or simply which was probably what Prove It intended.
I've always liked this proof that an irrational to an irrational power need not be irrational: consider . If that's rational, then we have our counterexample; otherwise, a counterexample is .
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