
Re: Matheology § 200
Posted:
Jan 26, 2013 7:06 AM


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.

