Find an irrational number whose binary development does not contain

zuzogiecwu

zuzogiecwu

Answered question

2022-05-15

Find an irrational number whose binary development does not contain strings of 0s or 1s of arbitrary length

Answer & Explanation

notemilyu1208

notemilyu1208

Beginner2022-05-16Added 20 answers

Consider 0. 10 ¯ 2 and change every 0 in position ( 2 n ) ! after the dot with a 1.
Such binary representation is aperiodic (so it gives an irrational number) and given by a concatenation of 0, 1 and 111 only. Additionally, such number is trascendental, as the sum between 2 3 and a Liouville number.
Alaina Holt

Alaina Holt

Beginner2022-05-17Added 3 answers

Call a = 101, b = 1001. Using only these two strings as "digits" write a non-repeating infinite pattern, for example
0. a b a a b a a a b a a a a b . . .
and then substitute a = 101, b = 1001.

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