Re: An uncountable countable set

In article <1157487601.440694.181380@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

Virgil schrieb:


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".

A set of elements E = (x1, x2, ..., x???, ...), which depend of
infinitely many co-ordinates x1, x2, ... x???, ... where each
co-ordinate is either m or w.

In somewhat more modern terms, the set of all functions f:N -> {"m","w"}
or equivalently the set of all functions g:N -> {0,1}

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

even when Cantor's proof is wrong and WM's proof is correct.

Regards, WM
.