Re: Cantor Confusion


mueckenh@xxxxxxxxxxxxxxxxx kirjoitti:

Newberry schrieb:

Sorry that I joined a bit late.
Doesn't matter.

Are you saying that (in an infinite
binary tree) the set of paths is uncountable but the set of edges is
countable?

The set of edges is obviously countable by, e.g.,

1, 2,
3,4,5,6,
7,...

As no path can separate from another one without the existence of two
more edges, the number of edges is an upper bound for the number of
paths.

The edges and paths are there completely from the beginning. Every two
paths separete on some finite level edge, but only when you got the
whole countably infinite path (the union of it`s all finite subpaths
starting from the beginning) all infinite long pathes separate from
each other. (In what you are doing you don`t have to care about finite
pathes)




Regards, WM

.

Quantcast