Cantor Confusion
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From: Eckard Blumschein on 27 Nov 2006 10:04 On 11/27/2006 2:08 PM, Bob Kolker wrote: > Eckard Blumschein wrote: >> On 11/26/2006 3:25 AM, Dik T. Winter wrote: >> >>>Remove all irrational points and in addition those >>>points that have x = 0. You have a disconnected set. >> >> >> A set is thought of elements put into it. Can you really set irreal >> points into it? >> This cannot work because the set has to have an order p/q. Otherwise it >> is not a set but a continuum. > > A continuum is a compact connected metric space. > > Learn some mathematics. I only learned discussion with you is wasted time. Continuum is a much older and more comprehensive concept than metric space and compatification. > > Bob Kolker > >> >>
From: mueckenh on 27 Nov 2006 10:33 Ralf Bader schrieb: > mueckenh(a)rz.fh-augsburg.de wrote: > > > > > Dik T. Winter schrieb: > > > >> In article <1164281187.964067.115190(a)m7g2000cwm.googlegroups.com> > >> mueckenh(a)rz.fh-augsburg.de writes: ... > >> > Cantor wrote: "It is remarkable that removing a countable set leaves > >> > the plaine *being connected*." But it is not remarkable that removing > >> > an uncountable set leaves the plaine being connected? What a foolish > >> > assertion. > >> > >> But removing an uncountable set can leave the plane either connected or > >> disconnected. What is remarkable about that? > > > > Nothing. In order to discuss Cantors paper one should know it. Of > > course Cantor knew your trivial example and those proposed by Mr. > > Bader, who is seems to be used to take trivialities for the main issue. > > Concerning Cantor, he either knew my example (which was trivial on purpose > in order to make it a sure bet that he knew it) Your example is in fact trivial: "E.g. the points inside a circle or rectangle, and I'm pretty sure that Cantor was aware of this." But it is even more trivial to see that Cantor did not consider it at all because he required the removed set do be dense in the whole plane. I wrote that already in the text wisely snipped by you. Of course you cannot agree to having been mistaken. O perhaps you really don't recognize it? A merciful hint: To concentrate the words babble, imbecile mess, idiotic, foolish, stupid within few lines is not very convincing. And slandering in a math newsgroup is not very impressive if the slanderer mistakes the set of rational numbers for the set of algebraic numbers. BTW: Have you meanwhile learnt to recognize the Greek letter xi and to distinguish it from the Greek letter zeta? Regards, WM
From: Franziska Neugebauer on 27 Nov 2006 13:14 mueckenh(a)rz.fh-augsburg.de wrote: > Franziska Neugebauer schrieb: >> mueckenh(a)rz.fh-augsburg.de wrote: >> >> > If the set 1,2,3,...,n is finite, then the set 1,2,3,..., n+1 is >> > finite too. >> > Therefore, by induction we (that is: those who can think logically) >> > prove that the generated set is always finite. >> >> Any set {0, 1, 2, ..., n} n e omega is finite. You have not proved >> that the set of all such sets { {}, {0}, {0, 1}, {0, 1, 2}, ... } is >> finite. > > I am only interested in sets of he form {1,2,3,..., n}. Only such sets > can be generated by induction. It is true that by applying the successor operation to the empty set only finite sets can be "generated". Infinitely many thereof. > Their finiteness is sufficient for my purposes. What are your purposes? F. N. -- xyz
From: Lester Zick on 27 Nov 2006 13:52 On 26 Nov 2006 14:04:18 -0800, "Jacko" <jackokring(a)gmail.com> wrote: >hi > >just to clarify pi has a power series, all rational coefficients can be >common denominatored. therefore the rational for pi has an infinite >denominator. hence my term infinite rational, hence countable of order >Z*Z. and this makes sense, and needs no proof by negation which would >be suseptable to godelian not not red = green. > >and that euclidean to hyperbolic space squre circles thing ... are you >guys losing it? Not sure to whom you're replying or why. I simply asked why square circles are inconceivable. Dik seems to think they aren't. Can't tell why. None of what you say here seems to have any bearing. ~v~~
From: Lester Zick on 27 Nov 2006 14:01
On Mon, 27 Nov 2006 07:25:21 -0500, Bob Kolker <nowhere(a)nowhere.com> wrote: >Eckard Blumschein wrote: >> >> >> Geometry is not outside mathematics. > >True. But Geometry is not all of mathematics either. Nor is arithmetic. >The two historical sources of mathematics has been land measurement and >counting objects. After which comes tracking the cycles in the heavens. So what? One historical source for chemistry was alchemy. Historical origins don't have any bearing on the nature of a science. ~v~~ |