In article <1ae6a5ac-811c-4ed4-b87f-3d686c8d35b7@e25g2000vbm.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 21 Nov., 17:41, William Hughes <wpihug...@gmail.com> wrote: > > On Nov 21, 12:00 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 21 Nov., 16:54, William Hughes <wpihug...@gmail.com> wrote: > > > > <snip> > > > > > > The limit is {}. {} is not a real number. {} does not have a > > > > reciprocal > > > > > But the numbers allowed by an empty set of decimal left to the point > > > has a reciprocal, namely a value larger than 1. > > > > Absolute nonsense. There are no numbers "allowed by an empty set". > > How can a set consisting of no numbers have a reciprocal? > > Not nonsense but as usual you have not understaood. > There are not numerals left of the decimal point, but there may be > numerals right of the decimal point. So there is a reciprocal of > 0.abc... between 1 and oo.
Since the so-called "digits" on either side of what you miscall a "decimal" point eventually exceed every finite quantity, whatever else that point may be, it is not a decimal point.
At least not outside of Wolkenmuekenheim! > > But that is not so important. Important and mathematical is only this: > > Every infinite sequence of real numbers either has no limit or has a > limit in the real numbers or the improper limit oo. In any case there > are never two or more limits! If existing, it can be calculated > according to Cauchy. If set theory supplies a tool, then the limit can > be calculated according to Cantor too. Or we can find some > restrictions in this way. > > Here we find a funny result like that: Cauchy states, that there is a > house. Cantor says that there are no stones. WH says that there is no > contradiction.
Most houses outside of Wolkenmuekenheim are built of wood or brick or both so do not contradict anything but WMatheology. > > Of course everybody can claim what he likes. It is not very new. There > are some matheologians who claim that "there" are numbers which nobody > can name.
In fact anyone and everyone accepting any standard model of the real numbers system, and most non-standard models, knows that! --
