
Re: Uncountable Diagonal Problem
Posted:
Dec 30, 2012 9:59 PM


On Dec 30, 6:27 pm, forbisga...@gmail.com wrote: > On Sunday, December 30, 2012 4:24:27 PM UTC8, Ross A. Finlayson wrote: > > So, the megasequences of the nested interval endpoints would end with > > sidebyside endpoints? Or, does any ordinallyindexed sequence of > > all of a segment of reals necessarily contain duplicates? > > I'm having trouble interpretting this. > > Given any CIxT where x is some base, the sequence continuing with > (x1) at all leaf nodes beyond some node y is equivalent to > the numeric successor node for y followed by 0 at all leaf nodes > continuing from it. > > Is that what you said or were thinking?
Here, for the complete infinite binary tree, or CI2T, CIBT, that basically being the Cantor space {0,1}^oo, or all binary sequences: that naturally represents real numbers between zero and one, with duplicates where .01(1)... = .10(0)....
Here, I was wondering that for nested intervals in the transfinite, that the interval wouldn't be empty for two different endpoints (else it could be for a countable ordinal), that there would be a duplicate, i.e., that the wellordering of the reals could be onto yet not 11.
Of course I think EF is a function with range [0,1], that wellorders the unit interval of reals, with the caveat as above that it follows from an expanded definition of real number, while of course that it is standardly modeled by real functions.
So, are nested intervals in the transfinite: empty?
Regards,
Ross Finlayson

