On 23 Dez., 21:20, Zuhair <zaljo...@gmail.com> wrote:
> Also the proof of Cantor is actually about uncountability of paths > that are distinguishable on finite basis.
That is the point! > > So how come we can have uncountably many distinguishable paths on > finite basis while finite distinguishability itself is countable? what > is the source for the extra distinguishability over the finite level? > we don't have any node at infinite level???
The source is the belief that a set can be finished (1) without being finished (2). (1) We can be sure that the complete set does not contain a certain number (the diagonal). (2) We can be sure that for every line of the following list, there is another line
0.0 0.1 0.11 0.111 ...
such that the diagonal constructed up to line n, 0.111...1, is not in the list as an entry (the entry of the next line) but is distinct from every line entry.
> > One of course can easily say that at actual infinity level some > results are COUNTER-INTUITIVE, and would say that the above aspect is > among those counter-intuitive aspects, much like a set having an equal > size to some proper superset. But I must confess that the above line > of counter-intuitiveness is too puzzling to me??? There must be > something that I'm missing? > > Any insights?
This posting by you presents a higher level of insight than most leading matheologians have acquired during their whole life time.
There is nothing to happen "in the infinite". And it is completely irrelevant whether the paths after the distinction are finite or infinite. Everything that happens in a Cantor-list and in a Binary Tree happens at a finite level.
Wait a few days until the shock will have diminished. Transfinity is nonsense!