Cantor Confusion
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From: Han.deBruijn on 14 Oct 2006 16:21 Virgil schreef: > In article <ecef7$452f4eb8$82a1e228$2523(a)news2.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > Virgil wrote: > > > > > In article <1160648741.707624.62340(a)m7g2000cwm.googlegroups.com>, > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > > >>Apply your knowledge to the balls of the vase. > > > > > > Which knowledge tells me that at noon each and every ball has been > > > removed from the vase. > > > > Not AT noon but BEFORE noon. True then. And ten other balls have been > > inserted. > > All of which will be removed before noon, as will any others inserted. > > > > > those times do not include noon or go past noon. > > > > True. Because those times are a FAKE. > > > > > You are assuming properties not given. > > > > No. YOU are assuming properties not given: _you_ are assuming that your > > fake parameter falsely called time has the properties of physical time, > > such that it can pass through noon, which it cannot. > > I am assuming time is a real valued variable which can take any real > value including 0 and positive values. Time is much more complicated than this. That's why your time is fake. Han de Bruijn
From: mueckenh on 14 Oct 2006 16:22 William Hughes schrieb: > > > What paradox? > > > > The result Lim{n-->oo} 9n = 0 where mathematics leads to Lim{n-->oo} > > 1/9n = 0. > > No, in mathematics Lim{n->oo} 9n = oo. Since the number of balls > in the vase at noon has nothing to do with Lim{n->oo} 9n LOL. You rather wanted to say: Since set theory has nothing to do with mathematics? >, a claim > that the number of balls in the vase at noon is 0 is not a claim > that Lim{n->oo} 9n = 0. By this arguing there can never be any contradictions in set theory. Any theory which cannot be falsified is a religion. "...classical logic was abstracted from the mathematics of finite sets and their subsets... Forgetful of this limited origin, one afterwards mistook that logic for something above and prior to all mathematics, and finally applied it, without justification, to the mathematics of infinite sets. This is the Fall and original sin of [Cantor's] set theory ..." (Weyl) Regards, WM
From: Virgil on 14 Oct 2006 16:24 In article <1160813914.000981.182690(a)e3g2000cwe.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > > > Cantor merely assumes, as do most mathematicians, that in mathematics, > > as contrasted with physics, there need not ever be a last significant > > digit in a decimal expansion. > > But this assumption is wrong as we obtain from the fact that > elimination of all factors 10^(-n) leads to undefined results. As in mathematics one does not need to "eliminate all factors 10^(-n)", or whatever idiocies physicists would impose on the non-physical, one also does not need to concede undefined results.
From: Virgil on 14 Oct 2006 16:26 In article <1160814074.566085.165200(a)b28g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > David Marcus schrieb: > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > David Marcus schrieb: > > > > Please state an internal contradiction of set theory. Please use the > > > > standard language of set theory/mathematics so that we can understand > > > > what the contradiction is without needing to ask what all the words > > > > mean. > > > > > > Good heavens, there are so many. Where shall I start with? > > > > > Consider the binary tree which has (no finite paths but only) infinite > > > paths representing the real numbers between 0 and 1. The edges (like a, > > > b, and c below) connect the nodes, i.e., the binary digits. The set of > > > edges is countable, because we can enumerate them > > > > > > 0. > > > /a\ > > > 0 1 > > > /b\c /\ > > > 0 1 0 1 > > > ............. > > > > > > Now we set up a relation between paths and edges. Relate edge a to all > > > paths which begin with 0.0. Relate edge b to all paths which begin with > > > 0.00 and relate edge c to all paths which begin with 0.01. Half of edge > > > a is inherited by all paths which begin with 0.00, the other half of > > > edge a is inherited by all paths which begin with 0.01. Continuing in > > > this manner in infinity, we see that every single infinite path is > > > related to 1 + 1/2 + 1/ 4 + ... = 2 edges, which are not related to any > > > other path. > > > > Are you using "relation" in its mathematical sense? > > Of course. But instead of whole elements, I consider fractions. That is > new but neither undefined nor wrong. > > > > Please define your terms "half an edge" and "inherited". > > I can't believe that you are unable to understand what "half" or > "inherited" means. > I rather believe you don't want to understand it. Therefore an > explanation will not help much. Which unwillingness/inability to explain reveals their lack of meaning.
From: Han.deBruijn on 14 Oct 2006 16:26
Virgil schreef: > > In article <990aa$452e542e$82a1e228$16180(a)news1.tudelft.nl>, > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > > > > sqrt(-1) doesn't exist either. Frankly, I have a much harder time > > believing in "imaginary" numbers than I do believing in infinite > > sets. Hey! Hey! Another debater said this. Not me! > Much of electronics development over the last couple of centuries is > highly dependent on the "existence" of sqrt(-1). Does HdB not believe in > FM radio, TV, radar, etc. Han de Bruijn |