
Re: Matheology § 200
Posted:
Jan 26, 2013 4:40 PM


On 26 Jan., 16:08, William Hughes <wpihug...@gmail.com> wrote: > On Jan 26, 1:42 pm, WM <mueck...@rz.fhaugsburg.de> wrote: > > > > > > > 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. > > Nope. The limit is a single number. In analysis there is no > limit set.
Like to drop logic? Nobody can hinder you. In analysis the limit is a single number, not a real though, that consists of infinitely many indexed digits. In analysis the set of indices can be calculated. Even if William Hughes tries to forbid that.
Regards, WM

