On 11 Jun., 00:12, William Hughes <wpihug...@hotmail.com> wrote:
> - There is more that one path through "that node" > > - There are countably many nodes below "that node" > > - Assuming that "For the others we > will find other nodes, below that one chosen" > is equivalent to assuming that there are only > countably many paths through "that node"
No. It is not assuming this but *proving* this. Because paths cannot be distinguished without nodes.
Equivalently: Assuming that that, in Cantor's proof, every line contains a digit that differs from the corresponding digit of the anti diagonal would be assuming that the anti diagonal is not in the list. > > - You are trying to prove that there are countably many > paths through the root node. > > - This is equivalent to proving that there are countably many > paths through "that node"
This is equivalent to proving that there are only countably many possibilities of distinguishing paths below "that node".
