On 1 Feb., 14:43, harry_potte...@walla.co.il wrote:
> > First of all, I don't and I can't talk for those eminent authorities, though I don't think there are many that "defend the existence of an omega-th level in any binary tree" anymore than "many" of them would be ready to defend "the existence of the first (in the usual natural order) positive real number", or the existence of "the infinite-th negative natural number". > These filological, semi-logical, semantic nonsenses fit yours, and they are exterior, and seriously unimportant, to mathematics.
My question: How can we distinguish between that infinite binary tree that contains only all finite initial segments of the infinite paths and the complete infinite binary tree that in addition also contains all infinite paths?
One tree is <? 2 ; the other is ?? 2 , which has ? 2 as its top level, sitting above the levels of <? 2 . Similarly, ?2 2 , the complete binary tree of height 3 , differs from <2 2 , the complete binary tree of height 2 , by having 2 2 as its top level, sitting above both levels of <2 2 . ? Brian M. Scott 7 hours ago