Prove: for any two real numbers a

Mohammad Cannon

Mohammad Cannon

Answered question

2022-06-27

Prove: for any two real numbers a , b R we may find a both a rational and irrational number between them.

Answer & Explanation

kejohananws

kejohananws

Beginner2022-06-28Added 19 answers

You can use the Archimedean property of R . Take b > a. There is some n such that 2 n < b a. There are at least two rationals with denominator n between a and b. Then the lower one plus 2 1 n is an irrational between a and b

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