Re: An uncountable countable set

In article <1157367467.816725.158560@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:


Cantor's list has as many lines as my tree.

But not as many "lines" as MY tree has paths.




Again, the second proof was *not* about the reals.

Please spare your nonsense. Cantor did not consider anything else than
the reals.



Cantor's "diagonal" proof did not even concern them. It was others who
later applied it to the set of reals. it was originally about the set of
all lists (functions with domain N) or strings from an "alphabet" of two
"letters".

If one considers the alphabet of {"L","R"} for left branch and right
branch, Cantor's original proof essentially proves that the number of
paths in an infinite binary tree is uncountable.


Give my a tree of infinite paths consisting of 0's and 1's, and I show
that there
are not less edges than paths.

Cantor shows less edges than paths. In a choice between a proof by
Cantor and a proof by "Mueckenh", I will choose Cantor every time.

Give up your arguing. All set theorists know that the edges of my tree
are countable. Even Virgil knows it.


But everyone knows that the set of paths is uncountable. Even Cantor has
proved it.
.

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