In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 26 Jan., 13:06, William Hughes <wpihug...@gmail.com> wrote: > > On Jan 26, 12:52 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > > > > > > > On 26 Jan., 12:31, William Hughes <wpihug...@gmail.com> wrote: > > > > > > On Jan 26, 9:24 am, WM <mueck...@rz.fh-augsburg.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 counter-intuitive, > > > > > > Correct. But counter-intuitive 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.
I know of no such definition of any limit process. > > > > > Obviously you have not yet understood?
Why bother to understand nonsense?
> > > In my proof the cardinality of the limit in set theory and the > > > cardinality of the limit in analysis are different.
Your proof, as usual, is only valid in your own private world of Wolkenmuekenheim > > > > 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.
Then, according to WM, lim_(n -> oo) 1/n must have infinitely many bits.
> 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.