
Re: Matheology § 200
Posted:
Jan 26, 2013 7:54 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. > > > 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.
In order to correct your mistake, here are the details. In my proof we have: 1) The limit of the cardinals in set theory: aleph_0 2) The cardinality of the limit in set theory: 0 3) The limit of the number of digits in analysis: oo 4) The number of digits of the limit in analysis: oo
There is only one nonsensical result. But it is necessary to assume (2) in order to get the desired result Card(N) = Card(Q).
Regards, WM

