On Friday, 19 July 2013 22:18:49 UTC+2, Michael Klemm wrote: > Path have verices and edges and real numbers have no such things.
It is hard to confess that Cantor's theory is a mess, isn't it. Therefore you even take the trouble to out yourself as a clown who cannot see the parallel between paths and numbers, between nodes and bits.
>>> 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.
I could, if I would, but I won't. Paths and binary representations of real numbers of the unit inteval are isomorphic.
And there is no mathematical explanation why lists of rationals do not contain what trees of rationals do contain.
By the way, have you ever tried to apply Cantor's diagonal argument on the set of all defined numbers? You know what it means when anumber is defined? There is no escape into the indefinability of definability, which is advocated by the fools of mythologic. Here we have only defined numbers. And do you know what the anti-diagonal of such a list is? It is a defined number. So application of Cantor on defined numbers shows that they are uncountable.