Cantor Confusion
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From: MoeBlee on 4 Oct 2006 11:56 Albrecht wrote: > MoeBlee schrieb: > > > Albrecht wrote: > > > > > I will try to explain my claim again: There is only a[n] [anti-]diagonal number > > > which is proveable not in the list if there is a real number which is > > > build up out of all the real numbers in the list. But for an infinite > > > list you can't end the diagonal number. You may have a sequence which > > > converge. But you never have a limit. > > > > Then you're not talking about the reals. > > The points on a straight line are representations of the reals. Do you > think so? No, I don't think they are "representations" of real numbers. In analytic geometry, in, for example, the plane R2, they are ordered pairs of real numbers. > With Cantor you have to think that some points on the > straight line (to be exact: the absolute majority of them) are not > reachable by construction. > Should this be a consequence of an useful mathematics? Give me your axiomatization that is rich enough for ordinary calculus, and with a mathematical definition of 'constructible', and such that every real number is constructible. Then we'll talk about that. > Are the consequences you claim for the Cantor proof really needful? I > don't think so. Whether needed or not, given an axiomatization, they're theorems. > There are many examples in which the systemes break down in > extrapolation to infinity. Let's have the sequence of polygones in the > circle which numbers of edges run up to infinity. Extrapolate the areas > to the limite case and you will get the area of the circle. Isn't it > rational to think that the the circle is identic with the limit case of > the polygones? Isn't it rational to think that the limit case of the > polygones is a polygone with (countable) infinite edges and this edges > are identical with (all) the points on the circle line? Since we don't even agree as to what a real number is, I can't imagine a discussion with you about the above. > Concerning Cantors diagonal argument: Can we rational speak about > convergence if we don't have a (finite) law which gives us endlessly > the converging values? I don't know what you mean by "endlessly converging values". What is the difference between converging and "endlessly converging"? MoeBlee
From: guenther vonKnakspot on 4 Oct 2006 12:05 Albrecht wrote: > MoeBlee schrieb: > > > Albrecht wrote: > > > > > I will try to explain my claim again: There is only a[n] [anti-]diagonal number > > > which is proveable not in the list if there is a real number which is > > > build up out of all the real numbers in the list. But for an infinite > > > list you can't end the diagonal number. You may have a sequence which > > > converge. But you never have a limit. > > > > Then you're not talking about the reals. > > The points on a straight line are representations of the reals. Do you No, points are points, numbers are numbers and representations are representations. You can put the points on any straight line in a 1-1 relationship to the reals, but you can not put all finite representations into a 1-1 relationship with the reals or with the points on any straight line. Are you aware of this fact? You should try to absorb this notion, because it would most probably help you overcome the problems you have in dealing with all these notions. > think so? With Cantor you have to think that some points on the > straight line (to be exact: the absolute majority of them) are not > reachable by construction. > Should this be a consequence of an useful mathematics? Mathematics does not have to be useful. As it is, however, it is quite useful and that is exactly because it is as it is, not in spite of that fact. But it wouldn't be as soon as it was crippled in order to accomodate dimwits as yourself. And that is the main problem with your kind. You fail to understand counterintuitive concepts and demand that they be banned. Normal people would either learn until they understood, or wouldn't give a damn about such things, as in fact almost every human being does. > Are the consequences you claim for the Cantor proof really needful? I > don't think so. > There are many examples in which the systemes break down in > extrapolation to infinity. Let's have the sequence of polygones in the > circle which numbers of edges run up to infinity. Extrapolate the areas > to the limite case and you will get the area of the circle. Isn't it > rational to think that the the circle is identic with the limit case of > the polygones? Isn't it rational to think that the limit case of the > polygones is a polygone with (countable) infinite edges and this edges > are identical with (all) the points on the circle line? > > Concerning Cantors diagonal argument: Can we rational speak about > convergence if we don't have a (finite) law which gives us endlessly > the converging values? > > What do you think? That you are dumb because you are ignorant and instead of pursuing a remedy for your ignorance you choose to complain and demand that everyone be lowered to your own flawed standards. > > Best regards > Albrecht S. Storz >
From: Virgil on 4 Oct 2006 13:49 In article <647c1$45239e63$82a1e228$3519(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > One cannot speak of correct with a mathematics that is a non-discipline > and gives non-discplinary answers to ill-posed questions like this one: Whatever HdB was trying to say, in English it is nonsense.
From: David R Tribble on 4 Oct 2006 16:37 Albrecht wrote: >> The idea of "all infinite many objects" in any sense is >> self-contradicting. There is no "all" of infinite many things. > Han de Bruijn wrote: > Bravo! Another mathematician (?) who cares about disciplinary thinking. Let's see. If I define set N as containing "all" of the naturals, i.e., {0,1,2,3,...}, you're (both) saying that N can't exist as a real set, because there is no way to have "all" of an "infinitely many" elements at once. So then we must conclude that there are naturals that are not in N, because N can't contain all the (infinitely many) naturals. So now I define another set N' to contain all the naturals except those that are already in N, i.e., those naturals that we concluded must be omitted from N. So what is in this second set N'? Is it also not an infinite set?
From: georgie on 4 Oct 2006 16:47
Tonico wrote: > georgie wrote: > > So you read hundreds of posts because you think poker is a troll > > but Virgil has added some real mathematics. I think you're sick. > *************************************************************************************** > I actually am kindda sick in my back. Thanx for worrying...:) > And I do NOT read "hundreds" of post, though you may believe I do. I > don't care. > And I don't know whether Virgil has added some "real" mathematics (as > opossed to nightmared mathematics or what?) or not: he seems to know > some set theory, and Poker doesn't. > And what hurts you so much about some people calling the joker a troll? > Do you feel that the adjective becomes you better than him/her or > perhaps he/she is your sweetheart and it makes your heart bleed reading > how much fun we make out of his nonsenses? > Regards > Tonio I can't recall seeing PJ's remarks all over the NG. Virgil's worthless statements seem to be everywhere. |