>> WM wrote: >>> Would you think that the Binary Tree containing only all rational >>> numbers is impossible? > >> A binary tree containing all finite initial path segments of the complete >> binary tree contains, although no rational numbers, > > That is correct. Real numbers cannot be defined by finite initial segments > of infinite paths (and they cannot be defined by infinite paths). Every > real number needs a finite definition like "0.5 and only zeros following".
Path have verices and edges and real numbers have no such things.
>> a lot of other things, for example pairs of paths or paths beginnig on >> level 13 and ending on level 17. > > You appear to have your own understandig of "paths". A path in the > infinity Binary Tree is, in mathematics, an infinite path containing the > root node. Sometimes also finite initial segments are called paths, but > each one starts at the root node.
It is you who can not distinguish between paths with one end and paths with two ends.