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. > > 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.
You cannot be too unmathematical to miss the fact that every B_k contains a countable set of infinite paths, such that at least 100 nodes are missing which would be required - at least - this is a very rough estimation - to guarantee the existence of uncountably many infinite paths. Will you really claim incompetence of understanding that without a formal approach?
