Here jsfisher defines set A such that any member of set A < some Y, and he wants to show that A has no largest member.
You belabor the obvious.
By this construction it is clear that Y is not a member of A
More obvious belaborment.
...otherwise Y is the largest member of A and we cannot prove that A does not have the largest member.
(intermixed with gibberish)
Since Y must not be a member of A
(Note the use of bold. Clearly this is important.)
and A's members are non-finite R members
(infinitely many, actually.)
that each one of them < Y, then A members are some non-finite R elements that exist in the clopen interval [W,Y), where W is the smallest member of A set.
No. And I'll bet just about everyone except Doron knows why his statement is just wrong.
Now jsfisher provides the assumption, which claims that the non-finite set A that is based on the clopen interval [W,Y)
Nope.
has the largest member called Z, which is a member of A set (and an element of [W,Y) interval).
Nope.
Here we clearly see the open side ",Y)" of the clopen interval [W,Y), that jsfisher claims that this clopen interval is not a part of his proof.
Yes, indeed. It is not part of the proof. It is just some bit of irrelevance Doron keeps trying to introduce.
But the fact is that Z is a member of A and < Y, exactly because we deal here with the clopen interval [W,Y).
Nope.
We can clearly see that since A has no largest member
Excellent!! You have accepted the proof as valid. Ok, then, we are done. Doron accepts that {X : X < Y} has no largest element.
Why'd it take so long?
then jsfisher claim ( see
http://www.internationalskeptics.com/forums/showpost.php?p=4721582&postcount=2864 ) that Y is the immediate successor of A set ( that its members are the elements of the clopen interval [W,Y) ), is a false claim.
Whoa! Talk about a leap of mush into unrelated nonsense.... There is no logical connection between this and anything that preceded it. (And even if there were, since the premises are false, the conclusion would be irrelevant.)
By the way, I never claimed what Doron claims I have claimed, nor does the set have its elements entirely in the half-open interval [W, Y).
