On Jun 11, 6:21 am, WM <mueck...@rz.fh-augsburg.de> wrote: > 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"
We are discussing WM's statement:
Let us choose one of them and map it one that node. For the others we will find other nodes, below that one chosen.
WM has agreed
- There is more that one path through "that node"
- There are countably many nodes below "that node"
We are not at
> > - 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.
Nope, "assuming" is not "proving". You give a putative proof that starts out by assuming what you want to prove. This is circular.
> Because paths cannot be distinguished without nodes.
Proves nothing. We know that a countable number of elements can distinguish an uncountable number of subsets. A countable number of nodes can distinguish an uncountable number of paths.
