```Date: Nov 21, 2012 12:57 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 154: Consistency Proof!

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 onthe 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 thedecimal 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 accumulationpoints, If there is only one accumulation point, we call it the limitof 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 itthe only possible result of set theory? If the latter is true: Do youagree that we can state: Set theory is not suitable to determinerestrictions for limits of sequences?Regards, WM
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