
Re: Matheology § 200
Posted:
Jan 26, 2013 7:42 AM


On 26 Jan., 13:06, William Hughes <wpihug...@gmail.com> wrote: > On Jan 26, 12:52 pm, WM <mueck...@rz.fhaugsburg.de> wrote: > > > > > > > On 26 Jan., 12:31, William Hughes <wpihug...@gmail.com> wrote: > > > > On Jan 26, 9:24 am, WM <mueck...@rz.fhaugsburg.de> wrote: > > > > > Matheology § 200 > > > > > We know that the real numbers of set theory are very different from > > > > the real numbers of analysis, at least most of them, because we cannot > > > > use them. But it seems, that also the natural numbers of analysis 1, > > > > 2, 3, ... are different from the cardinal numbers 1, 2, 3, ... > > > > > This is a result of the story of Tristram Shandy, mentioned briefly in > > > > § 077 already, who, according to Fraenkel and Levy ["Abstract Set > > > > Theory" (1976), p. 30] "writes his autobiography so pedantically that > > > > the description of each day takes him a year. If he is mortal he can > > > > never terminate; but if he lived forever then no part of his biography > > > > would remain unwritten, for to each day of his life a year devoted to > > > > that day's description would correspond." > > > > > This result is counterintuitive, > > > > Correct. But counterintuitive does not mean contradictory. > > > Outside of Wolkenmeukenheim, the limit of cardinalites is not > > > necessarily equal to the cardinality of the limit.
Aside: Of course this nonsense shows already that set theory is such. A limit is the continuation of the finite into the infinite. But that is not used in my proof. > > > Obviously you have not yet understood? > > In my proof the cardinality of the limit in set theory and the > > cardinality of the limit in analysis are different. > > Nope In analysis you take the cardinalities > of a sequence of sets, i.e. take a sequence of numbers, > and calculate a limit. However, this limit is not the > cardinality of a limit set. > In anylysis you calculate > the limit of the cardinalities not the cardinality of > the limit.
You are not well informed. Read my proof again (and again, if necessary, until you will have understood, if possible): In analysis you calculate the limit. This limit contains numbers or (in the reduced case of my proof) bits 0 and 1. The number of theses bits is the cardinality of the limit. In set theory it is similar. The number of bits in the limit set is the cardinality of the limit set. And that is oo in analysis and it is empty in set theory.
Regards, WM

