Re: The complete infinite binary tree has only countably many infinite paths.

Dear Calvin,
there is no point of formalizing such an obvious truth as I have shown
by my three proofs in the initial posting. But I think that this
thread has yielded a lot of new insights for all parties. Perhaps you
will agree that when you first answered my FOM-contribution, you had
no clue what a multitude of facets the binary tree may hide, won't
you?

Regards, WM

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Personally speaking, I learned nothing from this thread, and it provided no new insights. I have heard this argument about binary trees many times before, and its probably been floating around for 100+ years. Anybody who has spent any time in sci.math or sci.logic would realise instantly that the counter-example of 1/3 will be raised, but instead of the crank admitting they have not formed a bijection between N and R, they will try and confuse their way out of it with some bull*** about 1/3 mapping to some number which is not part of N.

Happens every couple of months here. The informational or educational value of such threads is zero for anybody with the slightest knowledge of set theory.

Regards, PW

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