Is there a 'far' irrational number?

rmd1228887e

rmd1228887e

Answered question

2022-07-15

Is there a 'far' irrational number?

Answer & Explanation

Alexia Hart

Alexia Hart

Beginner2022-07-16Added 19 answers

Consider x = j = 1 a j / 4 j where each a j is either 1 or 2. Thus the binary expansion of x consists of two-digit blocks which are either 10 or 01. Then x is far. But there are uncountably many choices, so all but countably many of them are irrational.

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