In article <email@example.com>, firstname.lastname@example.org wrote:
> On Thursday, 27 February 2014 01:11:29 UTC+1, Martin Shobe wrote: > > > > >> What about sets being infinite but not Dedekind-infinite? > > > > > > > > > Can you give an example? > > > > > > > > You were told on math.stackexchange that you can't be given an explicit > > > > example. You were even told why. Why are you asking for an example here? > > They are not very bright there? Examples that can't be given explicit do not > belong to mathematics. But here we have a simple example: The set of real > numbers without the set of definable real numbers (definable in any language > that can be used) is infinite but not Dedekind infinite.
Does WM mean the set of real numbers that are not individually defineable, because the set of all real numbers is defineable as are, collectively, all of its members?
For example, each real number is either the least upper bound of a non-empty collection of rational numbers which is bounded above or the limit of a Cauchy sequence of rational numbers, depending on which definition of the real field one uses. --