On Sunday, 21 July 2013 05:06:42 UTC+2, Virgil wrote: > In article <email@example.com>, firstname.lastname@example.org wrote: > On Saturday, 20 July 2013 21:31:03 UTC+2, Virgil wrote:
>>> Any countable set can be listed without inclusion of any non-members.
> > at least if not
> Since the definition of "countable" requires the ability to surject |N to the the collection of whatever is alleged to be countable, there is no |not if".
The rationals are countable. If written in the Binary Tree just these aleph_0 elements remain aleph_0 elements, don't they? Do the rational points of the unit interval have a cardinality aleph_0? You think so.
But the rationals written in the Binary Tree create a set of cardinality larger than aleph_0. That is not of this world. It is