On Nov 21, 1:20 pm, WM <mueck...@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.
Nope. The limit of the set of digits to the left of the decimal point is not a set of digits to the right of the decimal. If we change the limit to the set of digits to the left or right of the decimal point we still get {}. {} is not a real number and does not have a reciprocal.
> So there is a reciprocal of > 0.abc... between 1 and oo. > > 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!
Piffle. You really know nothing about limits do you.
> 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.
