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June 23 Information

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) reply

Why did you write the decimal point as a comma?? Georgia guy ( talk) 10:52, 23 June 2021 (UTC) reply
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) reply
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) reply
Almost every real is normal in base 2.-- Antendren ( talk) 23:59, 23 June 2021 (UTC) reply
Also, 0.010101.. and so on (13 in base 2) is definitely not normal: the sequence "11" does not occur.  -- Lambiam 10:29, 24 June 2021 (UTC) reply
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) reply
(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) reply
From Wikipedia, the free encyclopedia
Mathematics desk
< June 22 << May | June | Jul >> June 24 >
Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.


June 23 Information

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) reply

Why did you write the decimal point as a comma?? Georgia guy ( talk) 10:52, 23 June 2021 (UTC) reply
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) reply
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) reply
Almost every real is normal in base 2.-- Antendren ( talk) 23:59, 23 June 2021 (UTC) reply
Also, 0.010101.. and so on (13 in base 2) is definitely not normal: the sequence "11" does not occur.  -- Lambiam 10:29, 24 June 2021 (UTC) reply
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) reply
(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) reply

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