Virgil
Posts:
9,012
Registered:
1/6/11


Re: Matheology sqrt(2): WM admits to unlistability of 0/1 sequences
Posted:
Dec 21, 2013 10:22 PM


In article <0012ac941e5b4cfeb06645a335fa78e9@googlegroups.com>, jonas.thornvall@gmail.com wrote:
> Den lördagen den 21:e december 2013 kl. 23:35:43 UTC+1 skrev Virgil: > > In article <b518ea398daf465ab7004e9b46b446cf@googlegroups.com>,
> > jonas.thornvall@gmail.com wrote:
> > > > According to mainstream math 0.999... is to be equal to 1, although i > > > > just
> > > > proved it never will.
> > > You can not claim that a list generating nonzero terms to be equal to > > > zero.
> > > Thus the subtraction will never yield zero not ever after infinitly many
> > > subtraction, whatever that is supposed to be in your fairynumber world.
> > In mathematics, 0.999... represents either an infinite sequence of
> > values or the limit value of such a sequence.
> > In that latter case, the value is 1.
> > So when speaking of "the value of 0.999...", one should be able to
> > deduce that that limit value is what is meant.
> > WM is apparently not able to deduce that.
> > 
> I do not see how he could the calculation you stipulate to become zero after > infinitly many iterations. Will still yield infinitly many preceding zeros > +1.
In article <0012ac941e5b4cfeb06645a335fa78e9@googlegroups.com>, jonas.thornvall@gmail.com wrote: > Den lördagen den 21:e december 2013 kl. 23:35:43 UTC+1 skrev Virgil: > > In article <b518ea398daf465ab7004e9b46b446cf@googlegroups.com>, > > jonas.thornvall@gmail.com wrote: > > > > According to mainstream math 0.999... is to be equal to 1, although i > > > > just > > > > proved it never will. > > > You can not claim that a list generating nonzero terms to be equal to > > > zero. > > > Thus the subtraction will never yield zero not ever after infinitly many > > > subtraction, whatever that is supposed to be in your fairynumber world. > > In mathematics, 0.999... represents either an infinite sequence of > > values or the limit value of such a sequence. > > In that latter case, the value is 1. > > So when speaking of "the value of 0.999...", one should be able to > > deduce that that limit value is what is meant. > > WM is apparently not able to deduce that. > >  > I do not see how he could the calculation you stipulate to become zero after > infinitly many iterations.
In standard mathematics an infinite sequence converges to a limit value, L, if and only if every neighborhood of that limit value L (open set containing L) also contains all but finitely many of the terms of the sequence. That does not require anything to become zero, even after infinitely many iterations.
Will still yield infinitly many preceding zeros > +1. 

