On Saturday, January 26, 2013 10:24:04 AM UTC+2, WM 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, but set theory needs the feature of > > completeness for the enumeration of all rational numbers. If not all > > could be enumerated, the same cardinality of |Q and |N could not be > > proved. > > > > However recently a formal contradiction with the corresponding limit > > of real analysis could be shown: > > http://planetmath.org/?op=getobj&from=objects&id=12607 > > and here > > http://www.hs-augsburg.de/medium/download/oeffentlichkeitsarbeit/publikationen/forschungsbericht_2012.pdf > > on p. 242 - 244 > > The limit of remaining unwritten days is infinite according to > > analysis whereas Fraenkel's story is approved by set theory. > > > > Nevertheless, matheologians deny every contradiction. One of them, > > Michael Greinecker (as a self-proclaimed watchdog, and bouncer in > > MathOverflow > > http://meta.mathoverflow.net/discussion/1296/crank-post-to-flag-as-spam/#Item_0 > > an interbreeding of Tomás de Torquemada and Lawrenti Beria) stated: > > "there is no contradiction. Just a somewhat surprising result.
Poor WM: his last intent to have some of his trash published in SE received a rather quick "close thread" and, as with any otherclsoed threads, it vanished into oblivion.