Virgil
Posts:
7,021
Registered:
1/6/11


Re: Matheology � 295
Posted:
Jun 27, 2013 7:21 PM


In article <18d7cffcceb141dea1749f7e2dee64bc@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Thursday, 27 June 2013 02:37:17 UTC+2, Zeit Geist wrote: > > On Wednesday, June 26, 2013 8:12:09 AM UTC7, muec...@rz.fhaugsburg.de > > wrote: > On Tuesday, 25 June 2013 02:21:13 UTC+2, Zeit Geist wrote: > > > > > > > >> You think a sequence a, a, a, ... with a < 1 can, after formalization, > > >> have limit > 100? > > > > > > Probably not, > > > > > (except in case ZFC would suffer from that result, therefore your > > "probably") > > > > Let f:N\{0} U {N} > R, such for all n e N\{0}, f(n) = 1/n, and f(N) = 1. > > > Now, in the domain of the natural numbers as take as > a subdomain of the reals, lim f(x) as x > oo = 0, > but f(N) ~= 0.
While f(n) = 1/n, defines f(n) for each n which is a member of N, it does not define f(N), since N is a member of N.
Just another example of WM's logical and mathematical incompetence.
> I see.
No, you don't. The number of things about mathematics that you make a point of not seeing is far greater than the list of the few things you do understand about actual mathematics, rather than the ersatz matheology you propound.
> > In real mathematics there is no f(oo). Therefore it cannot differ from > lim{n>oo}f(n).
Which is in direct opposition to what WM has prevously claimed. > > Further the argument is required in set theory too. The diagonal differs from > the n first entries of the Cantorlist. The number of diagonals that are in > the first n lines of the list is a_n = 0 for the first n lines of the list: > 0, 0, 0, ... That sequence seems pretty well to imply that it holds for the > limit too That assumes a form of "continuity" at oo, which does not occur.
That infinitely many objects are not in any of an infinite increasing sequence of finite sets does not imply that there cannot be infinitely many members in the union of all those sets.
If each set in any infinite sequence of sets contains only one element not in any previous sets of that sequence, then both the limit set and the union set will contain infinitely many objects, at least everywhere outside of WM's incestuous matheology. 

