Cantor Confusion
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From: Eckard Blumschein on 21 Nov 2006 09:16 On 11/15/2006 1:49 AM, Virgil wrote: > mueckenh(a)rz.fh-augsburg.de wrote: >> Cantor wrote, for instance to Killing, on April 5, 1895: >> Was Herr Veronese dar?ber in seiner Schrift giebt, halte ich f?r >> Phantastereien und was er gegen mich darin vorbringt, ist unbegr?ndet. >> Ueber seine unendlich gro?en Zahlen sagt er, da? sie auf anderen >> Hypothesen aufgebaut seien, als die meinigen. Die meinigen beruhen aber >> auf gar keinen Hypothesen sondern sind unmittelbar aus dem nat?rlichen >> Mengenbegriff abgezogen; sie sind ebenso nothwendig und frei von >> Willk?r, wie die endlichen ganzen Zahlen. >> >> Briefly: My infinite numbers are founded only on the natural notion of >> sets. They are as necessary and free of arbitriness as the finite whole >> numbers. > > What Cantor may have said in 1895 need not be binding in 2006. May have said? He wrote it. It was not binding in 1895 either. However, the Utopia by Dedekind and Cantor was reformed but it never got rid of its basic mistakes. While most views of Veronese were largely correct, his infinitely large numbers are not better than those by Cantor.
From: Eckard Blumschein on 21 Nov 2006 09:22 On 11/16/2006 10:09 PM, david petry wrote: > Dik T. Winter wrote: > >> If you want to find absolute truth you should not look at mathematics. > > Perhaps we should replace "absolute truth" with "culturally neutral > truth", or in other words, truth without any cultural, religious, or > philosophical bias. We can reason about this concept by asking the > question: what will the mathematics of advanced alien civilizations > (i.e. from other planets) look like? Thinking about this question > leads most of us to believe that there is a core of mathematics which > every such civilization will accept. I wonder, this is a belief I am sharing wholehartedly. Otherwise I am a notoriously unbelieving person.
From: Heinz Mau on 21 Nov 2006 09:28 Am Tue, 21 Nov 2006 14:52:48 +0100 schrieb Eckard Blumschein: > Being admittedly not very familiar with set theory, I nonetheless wonder > if sets are considered like something going on forever. You are in special not very familiar with mathematics at all.
From: Heinz Mau on 21 Nov 2006 09:31 Am Tue, 21 Nov 2006 15:22:13 +0100 schrieb Eckard Blumschein: > I wonder, this is a belief I am sharing wholehartedly. > Otherwise I am a notoriously unbelieving person. Otherwise you are a very stupid person. First you dumped the german ng's and now you dump here. We did go through this all the time - but you are snotnosed and dumb.
From: Eckard Blumschein on 21 Nov 2006 09:49
On 11/2/2006 9:29 AM, Virgil wrote: >> > Since it _exists_ only as a gedankenexperiment, a sort of mental game, >> > such fears are irrelevant. >> >> Other fears are more relevant. Such as the fear that infinities in >> mathematics may easily lead to irrelevancies in physics (like e.g. >> with Black Holes or String Theory) > > As the almost universal consensus of astronomers now is that the center > of many, possibly most, galaxies is a huge black hole, and that many > larger stars too big to eventually collapse into neutron stars collapse > into black holes when they run out of fuel, it appears that HdB is the > unaware of what are irrelevancies in physics. > > So that HdB is hardly in a position to dictate what should be considered > irrelevancies in areas outside of his supposed area of expertise. Yes. There is widespread consensus about black holes to exist. What about white holes, they are perhaps nor many supporter. When we learn from history we have to realize widespread but unfounded and wrong consensus for more than 100 years declaring Ohm correct but Seebeck wrong. I do not trust in infinity in physics. Infinity and continuum are just ideal concepts. Reality is most likely different from these models. I would like to support Han because his expertise is much closer to physics than the horizont of pure mathematicans. Maybe he even feels equally reluctant to swallow |sign(0)|=0 like me. With aptly defined reals I prefer |sign(0)|=1. Han will possibly not trust me because practicians like him used to operate with numbers, with rational numbers of course. Regards, Eckard |