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To: lojban
Date: Fri, 7 Jul 2000 08:00:20 +0000
Subject: Re: [lojban] 2 maths questions
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From: C.D.Wright@SOLIPSYS.COMPULINK.CO.UK
> I want to able to say that
> the set of integers is twice as "thick" ("dense" is already used
> for a different property) as the set of evens, and that the set
> of evens is 500,000 times as "thick" as the set of multiples of
> one million.
Given two sets, S1 and S2, S1 is "k-thick" in S2 if
for every sequence of intervals (ai,bi) such that bi-ai
goes to infinity, the sequence of ratios of the sizes of
the intersections between S1 with (ai,bi), and S2 with
(ai,bi), has limit k.
By this definition the set of primes is 0-thick in the
integers, as is the set of powers of two. This is less
helpful than you probably want, but generally this sort
of definition can be made local.
--
\\// ze'uku ko jmive gi'e snada