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Deltahedron (talk | contribs) disjunctive sequence, cite Bugeaud (2012) |
Deltahedron (talk | contribs) complexity function of a real number, cite Bugeaud (2012) |
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The limit exists as the logarithm of the complexity function is [[Subadditivity|subadditive]].<ref name=PF4>Pytheas Fogg (2002) p.4</ref> Every real number between 0 and 1 occurs as the topological entry of some sequence.<ref name=CN169>Cassaigne & Nicolas (2010) p.169</ref>
For ''x'' a real number and ''b'' an integer ≥ 2 then the complexity function of ''x'' in base ''b'' is the complexity function ''p''(''x'',''b'',''n'') of the sequence of digits of ''x'' written in base ''b''.
If ''x'' is an [[irrational number]] then ''p''(''x'',''b'',''n'') ≥ ''n''+1; if ''x'' is [[rational number|rational]] then ''p''(''x'',''b'',''n'') ≤ ''C'' for some constant ''C'' depending on ''x'' and ''b''.<ref name=Bug91>Bugeaud (2012) p.91</ref>
==References==
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