On Saturday, 16 August 2014 21:49:10 UTC+2, Ben Bacarisse wrote: > email@example.com writes: > > > > > On Friday, 15 August 2014 22:32:19 UTC+2, Ben Bacarisse wrote: > > > > > > > > >> > What do you understand by my "misunderstanding"? > > >> > > >> Exactly what you said: that the sequence of cardinalities should have > > >> limit 0 if set theory was right. > > > > > > In fact, if the set limit was the set at omega. >
> You'd need to define the WMglish term "the set at omega". I explained > how set sequence limits can be defined in the little paper I wrote and > there is no "set at omega" involved.
You mean that paper that has been considered nonsense by everybody who read it?
> You are free to reject these > limits, or to label them with any WMglish adjective you like, but you > can't choose what set theory says about it's own definitions. > Set theory names the final set of all naturals omega. > > > >> Set theory says that the limit of > >> cardinalities (we are talking about s_n here, yes?) is exactly what you > >> expect it to be: oo > > > > > > What are the infinitely many elements that the cardinality measures? > > The limit does not measure anything, because there is no "final set" for > it to measure. That is the core of you misunderstanding.
It is also Cantor's misunderstanding. The set of all algebraics is a final set because every non-final set contains only a finite number of algebraics and does not allow for Cantor's "proof" of transcendentals.