Does every irrational number contain " 666 " in its

Anthony Kramer

Anthony Kramer

Answered question

2022-05-28

Does every irrational number contain " 666" in its decimal expansion?

Answer & Explanation

Hailee Henderson

Hailee Henderson

Beginner2022-05-29Added 12 answers

No. There are even transcendental numbers all of whose digits are 0 and 1.
Zeihergp

Zeihergp

Beginner2022-05-30Added 6 answers

For a concrete example, take
x = 0.101001000100001000001 1 00 0 n  zeros 1 00 0 n + 1  zeros 1 .
This decimal expansion isn't periodic (since it contains arbitrarily long runs of zeros), and so x is irrational. You can do something similar to avoid any string of digits you want, not just 666 666.

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