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