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.) > > > 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. > > Piffle.
A good argument. Possibly your last one. > > > Or we can find some > > restrictions in this way. > > Possibly, but we need more than handwaving.
Is the limit { } of the set of digits based upon handwawing or is it the only possible result of set theory? If the latter is true: Do you agree that we can state: Set theory is not suitable to determine restrictions for limits of sequences?
