In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 28 Nov., 13:48, William Hughes <wpihug...@gmail.com> wrote: > > On Nov 28, 2:43 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > Induction proves also: Every set of natural numbers is finite. > > > Why do you overlook this simple proof? > > > > No, what induction proves is that every set of natural numbers > > with a largest number is finite. > > And induction proves that every set of natural numbers has a largest > number. For every finite n also n + 1 is finite and the set containing > both, n and n + 1 ist finite too.
THE set containing n and n+1 is a myth everywhere outside of WM's WMytheology since there are and endless string of sets containing any n and its successor n+1. > > > Induction is agnostic on > > the question of whether there can be a set of natural numbers > > without largest number. > > That's because such a set is a contradiction.
That it contradicts mathematics is a lie, that it contradicts WM is a Mizva.
> Every number has a > magnitude, i.e. it is larger or smaller than another number. A set of > naturals without largest number is like a number without numerical > value or a word that can't be spelled.
Unless WM can name a "last" natural, there will always be a set with more naturals than WM can handle. And since any set of sets has a union set in mathematics, the union of all such sets of naturals does exist in mathematics. > > > The interesting thing is that > > you get the same "contradictions" whether or not you allow a > > set of natural numbers without largest number. > > You are wrong.
No WM is wrong!
> But that is not under discussion.
It is precisely what is under discussion.
> Under discussion is > the fact that set theory and analysis deliver different results.
Only because they are being asked different questions.
When asked the same question, they give the same answer.
> Or do > you continue to claim that analysis cannot determine that the limit of > my sequence has more than zero digits?
Until analysis can provide a decimal numeral representing the answer to your question, which will never happen, it cannot determine what you ask of it.
All analysis can say is that the limit must be "larger" than any value that a finite decimal numeral can represent, and thus cannot be given a decimal numeral representation.
That WM feels compelled to twist mathematics into exotic shapes to fit into his Wolkenmuekenheim is his problem, not ours, and not that of any actual mathematics. --