In article <a2670703-576c-4073-85ad-b214ad10c387@l18g2000vbv.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 21 Nov., 18:43, William Hughes <wpihug...@gmail.com> wrote: > > On Nov 21, 1:20 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > 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. > > Of course it is not, but it does not prohibit that there are digits on > the right. > > > 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. > > We cannot conclude from set theory that the digits on the right of the > decimal point vanish. > > > > > 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. > > In my book on analysis I write: a sequence may have many accumulation > points, If there is only one accumulation point, we call it the limit > of the sequence. (But I did not invent that definition.)
Just as well, as what you do invent is either not mathematics at all or merely very bad mathematics. --
