[Haskell-cafe] Re: Functional progr., infinity, and the Universe

[Bill Wood]

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