Wikipedia:Reference desk/Archives/Mathematics/2021 June 23

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June 23

Normal number to the base 2?

Beside the absoluty Normal Number, is there a normal number with base 2. So a binary normal number with 0,010101.. and so on.--2.200.60.148 (talk) 10:43, 23 June 2021 (UTC)

Why did you write the decimal point as a comma?? Georgia guy (talk) 10:52, 23 June 2021 (UTC)

Cause I'm German and there, its the usual notation. Sorry for that! — Preceding unsigned comment added by 2.200.60.148 (talk) 11:05, 23 June 2021 (UTC)

The construction given for the Champernowne constant works for all bases. See also OEIS sequence A066716 and Weisstein, Eric W. "Binary Champernowne Constant". MathWorld..  --Lambiam 12:50, 23 June 2021 (UTC)

Almost every real is normal in base 2.--Antendren (talk) 23:59, 23 June 2021 (UTC)

Also, 0.010101.. and so on (1⁄3 in base 2) is definitely not normal: the sequence "11" does not occur.  --Lambiam 10:29, 24 June 2021 (UTC)

In this cause, the Champernowne constant would be a absolut normal number. — Preceding unsigned comment added by 178.10.4.26 (talk) 14:19, 24 June 2021 (UTC)

(a) The Champernowne constant for which base? (For base 2, it equals 0.862240..., and for base 3, it equals 0.598958..., so the base makes a difference.) (b) How do you know (aka [citation needed])?  --Lambiam 14:58, 24 June 2021 (UTC)