In article <9104cca9-5758-460c-adb1-cb7c5d418eaa@j8g2000yqd.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 16 Jun., 19:45, MoeBlee <jazzm...@hotmail.com> wrote: > > > But, every countable set does have a bijection with N or has a > > bijection with some member of w (the set of natural numbers). > > That would be true if countability and aleph_0 were not self- > contradicting concepts. > > But there is a set that is less than uncountable but has no bijection > with N or a definasble subset of N. This set is the set of all finite > definitions (in binary representation). > > > 0 > 1 > 00 > 01 > ... >
WM declares that he has a list which is not, and cannot be, a list? > > where every line may be enumerated by an element of the countable set > omega^omega^omega (and, if required, finitely many more exponents for > alphabets, languages, dictionaries, thesauruses, and further > properties) > > > An obvious enumeration of the lines is 1, 2, 3, ... where every line > n > can have many sub-enumerations > > n > n.1.a > n.11.a > n.111.a > ...
Unless there are more than countably many subenumerations or more than countably many in one of them, the result is still countable.
