If you allow for bases to be real numbers, it is not guaranteed that natural numbers have a terminating expression. So is there a way to prove, that a number is not simply normal to any given base? Or is maybe even every number normal so some real base? How could you prove or disprove such a statement?
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Of bases for what are you talking? What is a "terminating expression? – trula Aug 16 '22 at 14:36
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2You might find my paper Absolutely abnormal numbers interesting—it discusses exactly this kind of question. – Greg Martin Aug 16 '22 at 15:32