Cantor Confusion
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From: Han de Bruijn on 4 Oct 2006 04:16 Albrecht wrote: > The idea of "all infinite many objects" in any sense is > self-contradicting. There is no "all" of infinite many things. Bravo! Another mathematician (?) who cares about disciplinary thinking. Han de Bruijn
From: Han de Bruijn on 4 Oct 2006 04:29 Albrecht wrote: > William Hughes wrote: > >>If you do not allow "completed infinite sets", then the meat >>of Cantor's proof (the cardinality of the reals is greater than >>that of the integers) cannot be done >>So, everyone who finds your "contradictions" to be convincing >>will find Cantor rather trivial. > > Any proof which shows that infinity is incomprehensible isn't trivial. > It must be a proof, which is working on the limit of the knowable. LIMIT is the keyword. All true knowledge about the infinite starts with finite things. The deep reason behind this is that infinity can never be observed in nature. Infinity is just an idealization of the finite which helps us to deal with "large quantities". That's why limits are the one and only sensible road to infinity. >>However, as far as I can see, 'everyone who finds your >>"contradictions" to be convincing', is a set with at most >>one element. > > Maybe. Wishful thinking on the part of William Hughes. A simple Google search will reveal that the army of 'sci.math' dissidents is steadily growing. Han de Bruijn
From: Han de Bruijn on 4 Oct 2006 04:34 Dik T. Winter wrote: > That is not the *mathematical* definition of "any". Any definition of Any is better than any mathematical definition of All. Han de Bruijn
From: Tonico on 4 Oct 2006 04:44 David R Tribble ha escrito: > Ross A. Finlayson wrote: > > Joker, and I've told people this before, please try and ignore Virgil. > > Why not ignore Poker Joker? At least Virgil knows set theory. > > Virgil, you really ought to refrain from feeding the trolls. > Their responses are only cluttering up the newsgroup. ************************************************************** I agree with David: Poker seems to have taken a step out of reason and maths and has begun a rather weird and pretty funny, in some cases, struggle against soundness and intelligence. I don't know Virgil but he knows some set theory, unlike the Joker, and any more addressing the joking messages from the joker is just feeding an already pretty fat troll. Better to leave the Joker alone; perhaps he'll meet JSH later at some stage in his trolling life and they'll be happy together thereafter... Regards Tonio
From: Tonico on 4 Oct 2006 04:59
Han de Bruijn ha escrito: > Wishful thinking on the part of William Hughes. A simple Google search > will reveal that the army of 'sci.math' dissidents is steadily growing. > > Han de Bruijn ************************************************** Zaas! Dissidents...from sci.math???? Didn't know somebody already formed a political or social or economical or whatever-that-isn't-science group called sci.math, and that it already has its dissidents! Perhaps Han means people that insist in talking about mathematics with some mathematicians from a non-mathematical point of view and without knowing mathematics? People that attack mathematicians and even mathematics (go figure!) when someone dares to point out some mathematical mistake in some nonsense that THEY say is correct IN SPITE of evidence in contrary? In the comic "Asterix" there appears a poet of a gale town about whose poetic talent the opinions are divided: he thinks he's a genius, ALL the other people think he stinks and is a pest, and many times they have to tie him up to a tree and and shut his mouth up with a sock so that he won't bother them. That's how many trolls in this sci.math behave: they think they are the best think that's happened to the world after the invention of warm water, but ANY mathematician know they're crackpots.... Oh well...trolls, as already stressed in another message, fulfill their role in these groups, too. Let's be nice to them....sort of. Regards Tonio |