Am 08.07.2014 11:57, schrieb firstname.lastname@example.org: > On Tuesday, 8 July 2014 10:14:23 UTC+2, karl wrote: > > >> >> The only thing you show is that a finite number of natural numbers is never >> enough to enumerate all rationals; nobody doubts that. > > Sorry, all finite natural numbers are not enough. If there are infinitely many, > why then should my proof for all not show it for all? >> > >> But for increasing n all rationals gets their index number. > > Not even in the limit, since in the limit the cardinality, i.e., >the number of not enumerated rationals is infinite.
This is your belief. in the enumeration given by Virgil
all rationals get their index here. Can you name any rational without an index? No, therefore you prove nothing, you only claim that something which is vaild for all finite natural numbers MUST BE TRUE also for something infinite. This is not correct.
>> >> All rationals get their index here. But, certainly, always for a >> given finite natural number there is an infinity of rationals which >> have indices larger than this number n. But this shows nothing. > > A proof for all n shows nothing?
It shows only that a finite number of naturals is not enough to provide indices for all rationals. That's it!!