Prove or disprove: For every irrational number x ,

Paiellorbkzp

Paiellorbkzp

Answered question

2022-06-01

Prove or disprove: For every irrational number x, there exists an irrational number y such that x y is a rational number.

Answer & Explanation

Sarahi Rollins

Sarahi Rollins

Beginner2022-06-02Added 2 answers

This raises the matter of defining x y for x < 0 and y not an integer. For x ( 0 , ) { 1 }, you can use a trick like the following. Observe that log 2 3 is irrational: in fact, 2 m 3 n for any n 0. Then, either log x 2 is rational or it isn't. If it is rational, then log x 2 log 2 3 = log x 3 is irrational.

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