[Haskell-cafe] Re: Functional progr., infinity, and the Universe
Bill Wood
william.wood3 at comcast.net
Fri Jun 23 10:23:59 EDT 2006
On Fri, 2006-06-23 at 09:38 -0400, Paul Hudak wrote:
. . .
> But the limit of a chain IS the maximal element of the set of all
> elements comprising the chain, since the LUB, in the case of a chain, is
> unique, and thus we don't have to worry about choosing the "least"
> element (i.e. it reduces to the upper bound, or maximal element).
There must be something additional going on, since in general the fact
that an ordered subset of a set has a LUB in the set does not imply that
the LUB is in the subset. For example, the subset {1 - 1/n : n in N+}
of Q has LUB = 1, but 1 is not an element of the subset. It would seem
that while the infinite list is the LUB of the chain of finite lists, it
is not itself a member of the chain of finite lists. So, what am I
missing?
-- Bill Wood
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