On Jul 15, 1:20 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 15 Jul., 19:26, MoeBlee <modem...@gmail.com> wrote: > > > On Jul 15, 11:12 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > even very unmathematical fellows can understand the > > > difference between potential and actual infinity and can see what this > > > figure means: > > > > 0, > > > / \ > > > 0 1 > > > / \ / \ > > > 0 1 0 1 > > > / > > > 0 ... > > > Indeed, I offered this exact formulation: > > > The complete binary tree is <S R> > > > where > > S = the set of finite binary sequences > > and > > R = {<x y> | x in S & y in S & x is a proper subset of y} > > > WM has not accepted that definition nor has he given a NON-ostensive > > NON-picture definition.
Of course, he skips that.
> > We could work without a precise definition if WM were mathematically > > mature enough not to present his arguments in vague, equivocal > > language. But in the circumstances with him, I believe it would be > > best to START the whole discussion about the tree by fixing a certain > > definite definition and then working, step by step through defintions > > of 'node', 'path', et. al and then step by step through the arguments > > about them, at each point, if necessary answering explicity as to what > > mathematical principle or logical rule has been used. That is > > basically the method of mathematics. WM, of course, won't do it. > > No. Too often I have made the experience that very tedious definitions > run through very many threads, some times through thousands of posts - > and after a while the oponent got tired or recognized his situation > and turned silent.
Yes, lots of posts spent (unsucessfully) trying to get WM to agree to and understand some basic mathematical defintions. Tedious, indeed.
Anyway, the definition I gave is only a couple of simple lines. Hardly tedious.
> You cannot be too unmathematical to miss the fact that every B_k > contains a countable set of infinite paths,
"contains". Element or subset?
Anyway no set that has as a member an infinite path is an element of, nor a subset of, any B_k.
