Absolutely Abnormal Numbers

Details Absolutely Abnormal Numbers Absolutely Abnormal Numbers

2000-06-12

arxiv.org/abs/math/0006089v2

Amer. Math. Monthly 108 (2001), no. 8, 746-754.

Mathematics

Number Theory

9 pages. The details of the main construction have changed somewhat, though the method of proof is the same. The paper has bee

Scientific paper

Despite the fact that almost all real numbers are absolutely normal---that is, the digits in their expansions to any base occur in all possible configurations with the expected frequency---not one specific example of an absolutely normal number is known. In this note we investigate the opposite extreme, numbers that are normal to no base whatsoever, and we succeed in writing down explicitly such a number.

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