Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Most numbers are not normal   We show, from a topological viewpoint, that most numbers are not normal in a
strong sense. More precisely, the set of numbers $x \in (0,1]$ with the
following property is comeager: for all integers $b\ge 2$ and $k\ge 1$, the
sequence of vectors made by the frequencies of all possibile strings of length
$k$ in the $b$-adic representation of $x$ has a maximal subset of accumulation
points, and each of them is the limit of a subsequence with an index set of
nonzero asymptotic density.
  This extends and provides a streamlined proof of the main result given by
Olsen in [Math. Proc. Cambridge Philos. Soc. 137 (2004), 43--53]. We provide
analogues in the context of analytic P-ideals and regular matrices.

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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg