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herbariak1

herbariak1

Answered question

2022-05-29

a 1 , a 2 , . . . . . . , a n are real numbers. Prove that there is a real number k such that a 1 + k , a 2 + k , , a n + k all are irrational.

Answer & Explanation

Syllingbs

Syllingbs

Beginner2022-05-30Added 11 answers

For a fixed i there are only countably many k such that a i + k is rational; call this set S i . But then S = S i is also countable, so it can not be all of R . Any k R S will work.

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