Jerzy Karczmarczuk wrote:
OK, I think that this subject matured enough to rest in peace...
I would have to agree with that, although...
Couldn't an infinite list just be regarded as the maximum element of
the (infinite) set of all finite lists?
Perhaps his intuition is right, but there are fundamental differences -
A. Between the chain of partial lists and the set of finite lists
Well, each partial list is finite. Of course it isn't the set of ALL
finite lists, but it is the set of all those finite lists that
approximate the given infinite list.
B. Between a limit and the maximum element of a set.
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).
So I'd say that Brian has at least come close to discovering God :-)
-Paul
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