Re: Cantor Confusion


*** T. Winter wrote:
In article <1167393772.865867.58640@xxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:

> A path is an (ordered) set. If there is no element distinguishing it
> from every other set, then it is not different from every other set.

Each path can be distinguished from each other path by some edge. There
is *no* edge that distinguishes a particular path from all other paths.
Back to that again. Quantifier dyslexia.

Similar to: each natural number written in decimal can be distinguished
from each other natural number by some (actually in most cases many)
decimal digit. For each natural number there is *no* decimal digit that
distinguishes it from all other decimal digits.

Even more trivially: let A = {a,b}, B = {b,c} and C = {c,a}. For each
set, there is no element that distingushes it from the other sets; yet
for each set can be distinguished from the others.

Cheers - Chas

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