Isn't it easy to describe such numbers? There are countably many requirements, and do one can enumerate digits do as to meet them all. Give each base infinitely many turns, and the add a big block of digits do as to interrupt the appearance of some fixed sequence.
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One can arrange that no digit or finite sequence in any base has convergent density.
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This is great! But shouldn't alpha2 be 3/4?
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Yes, I think that’s a typo.
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Actually I'm not getting an inkling of the abnormality of that number in base 10. Sure there are a lot of 9's in the decimal expansion at first, but what matters is the long run! I trust him, but I don't like this rhetorical tactic.
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Of course, maybe I'm missing the point!
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Unrelated: I am sure you know the story about the Champernowne number mentioned in the intro? I find it really cool.
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No, I don’t know the story. I know Champernowne was a friend of Turing, and he published his work on this constant when he was an undergraduate, but that exhausts my knowledge of the context.
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"the first few digits are..." (lists 23 billion digits)
Hvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi
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It's one of my favorite papers.
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I had fun extending Greg's result. I showed that there are numbers which are normal w.r.t the continued fraction expansion but not any base-b expansion. I just had to make one teeny tiny almost trivial assumption of the Generalized Riemann Hypothesis... https://arxiv.org/abs/1512.00337
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