Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Virgil
Posts:
8,833
Registered:
1/6/11


Re: Matheology � 300
Posted:
Jul 23, 2013 1:31 AM


In article <145ccf00437a4ba992c74dfaf133fd9f@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Monday, 22 July 2013 21:45:08 UTC+2, Virgil wrote: > > It is the structure of the Complete Infinite Binary Tree which cannot > > exist with only binary rational paths, since the existence of all the > > binary rational approximations to an irrational in such a tree requires > > the existence of the path for that irrational as well. > > Paths of irrationals in mathematics are not defined by "structure". That is > purest matheology.
They may not be in WM's wild weird world of WMytheology, but they are in the wider worlds of mathematics that allow such sets as N and 2^N. > > For every finite step n in the construction of the Binary Tree (by nodes or > by FIS or by paths of rationals), there is no irrational path. They sneak in > only after all finite steps.
Quite true.
But a binary tree cannot contain all finite paths without containing all infinite paths just like a unary tree cannot contain all FISONs as subsets without containing N.
> That is obvious nonsense. But if it was not > nonsense, then the same could happen in every Cantorlist. Not until lists (which are really just unary trees) become binary trees.
Which they are not. 



