> 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 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 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.