Cantor Confusion
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From: Bob Kolker on 15 Dec 2006 07:33 mueckenh(a)rz.fh-augsburg.de wrote: > > You map 10 digits on many more real numbers. Therefore not every real > numbers can get the shares of a full digit. An example: This is nonsense. Can you differentiate a digit from an finite or infinite sequence of digits? Bob Kolker
From: Bob Kolker on 15 Dec 2006 07:45 mueckenh(a)rz.fh-augsburg.de wrote: > > > Do you believe that today's standards are sound by tomorrow's > standards? Wait a day and we will find out. Hilbert's axiomatization of Euclidean Geometry done back in 1899 is as good today as it ever was. Aristotelean logic and semantics have held up very well over 2400 years. Too bad that Aristotelean physics fell way short. The difference between today's math and tomorrows math will be mostly in scope, not validity. The arithmetic argument that Euclid used to prove the infinitude of primes is as valid today as it was 2200 years ago. Bob Kolker
From: Han de Bruijn on 15 Dec 2006 08:23 William Hughes wrote: > Han de Bruijn wrote: > >>William Hughes wrote: >> >>>Han de Bruijn wrote: >>> >>>>William Hughes wrote: >>>> >>>>>Han de Bruijn wrote: >>>>> >>>>>>Let's repeat the question. Does there exist more than _one_ concept of >>>>>>infinity? Isn't unbounded the same as infinite = not finite = unlimited >>>>>>= without a limit? Please clarify to us what your "honest" thoughts are. >>>>> >>>>>You are *way* in deficit on clear answers. Try answering >>>>>the following question with yes or no. >>>>> >>>>> Is there a largest natural number? >>>> >>>>No. >>> >>>I there an unbounded set of natural numbers? >> >>Suppose you mean "Is". What does it mean that a set is unbounded? > > An unbounded set of natural numbers is a set of natural > numbers that does not have a largest element. > Please answer yes or no. No. Han de Bruijn
From: Dik T. Winter on 15 Dec 2006 08:54 In article <virgil-A4A26C.17473614122006(a)comcast.dca.giganews.com> Virgil <virgil(a)comcast.net> writes: > In article <1166109473.022083.10120(a)j72g2000cwa.googlegroups.com>, > mueckenh(a)rz.fh-augsburg.de wrote: .... > > The ordinal 2^omega is a countable set. Even omega^omega is a countable > > set. > > Not in ZFC or NBG. It is. Because it is not cardinal arithmetic but ordinal arithmetic. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
From: Dik T. Winter on 15 Dec 2006 10:17
In article <1166167313.573914.50760(a)j72g2000cwa.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: > cbrown(a)cbrownsystems.com schrieb: .... > > Unfortunately, following this link led me to a page saying "Das Buch > > ist nicht in unserer Datenbank gespeichert", which I don't understand, > > but guess means "That book is not in our database, sadly". > > Unfortunately this link was truncated. I try to post it again. I do not think that link makes much sense for somebody who does not understand the German sentence above. However, I do understand why you post that link. How much did publication cost you? My estimate is about EUR 1000. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ |