On Thursday, 27 February 2014 10:00:55 UTC+1, Virgil wrote: > In article <firstname.lastname@example.org>, > > email@example.com wrote: > > > On Thursday, 27 February 2014 01:48:53 UTC+1, Virgil wrote: > > > > In article <firstname.lastname@example.org>, > > > > email@example.com wrote: > > > > > You believe that all real numbers R except a countable set D are > > > > > undefinable. > > > > WRONG! > You have said so at least. But that does not bother you, of course. > > > > > > The reals are COLLECTIVELY defined > > > > > That does not make them enumerable. > > > > In fact, their verydefinition makes them non-numerable.
It makes them non-definable. > > > > > > by the standard definition of the > > > > field of real numbers, but that collective definition does not guarantee > > > > that each of them also has an individual definition separable from other > > > > individual definitions of all other real numbers. > > > > > Therefore they cannot be enumerated other than collectively by " 1 set". > > > > WRONG AGAIN! They cannot be ennumerated at all, but they can be referred > > to in various separate collections,
Countably many collections like everthing that can be referred to in mathematics. > > > > > > Similarly, Given a set of naturals numbers ther must be subsets of that > > > > set which cannot have finite definitions