In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> > When using induction you can only prove that a finite thing > > has some property. > > This can be proved for infinitely many finite things. > > > A collection such that for any n if n is in the > > collection then n+1 is in the collection is not finite. > > You cannot > > use induction to prove that you can remove this collection without > > changing the union. > > In fact I can use induction to show that actual infinity is nonsense
While no one could stop WM from doing so, if he had enough talent, he does not have enough talent.
Actual infiniteness makes more sense thatany of WM's idiotic alternaives.
: > An infinite but not actually infinite collection can be constructed
That is nonsense. At least outside Wolkenmuekenheim.
: > By induction I prove
No you don't!
: I put n without arriving at an infinite set, > and when n is put, I put n+1, also without arriving at an infinite > set. In this way I construct a (potentially) infinite collection > without reaching an actually infinite collection (that is a collection > the cardinality M of which is greater than all its elements: M > n for > all n).
WM then claims to be able to create a strictly increasing sequence having no maximal member whose limit he claims is no greater than some element in the sequence. Only in Wolkenmuekenheim. --