Re: Binary Tree and Pairs of Nodes

On Oct 14, 9:12 am, Herbert Newman <nomail@invalid> wrote:
In general: The n-th member in the sequence differs from 0.111... (at
least) at its (n+1)-th digit, for any n e IN. Hence 0.111... differs from
ALL members in the sequence (since there are no other members in it than
that one "indexed" by the natural numbers - by definition of "sequence").

It occurs to me that we need to start cataloging the modes of error
that anti-Cantorians usually make. There is the usual quantifer-
switching one. There is also the usual error of thinking that the
limit
of a sequence must automatically be a member of it, or must
automatically
be "covered" by it in some way.

WM's continued insistence on these fallacies in the face of clear
explanations is probably indicative of trolling.
He keeps trying to tell us that WE have to concede something because
"we can't" produce a counterexample to some irrelevant criterion that
he makes up. The fact that it is up TO US AND NOT him to decide
what a proof is seems to have quite completely escaped him.
.

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