Cantor Confusion
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From: Virgil on 16 Oct 2006 15:06 In article <18bda$45333c50$82a1e228$8972(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > David Marcus wrote: > > > Han.deBruijn(a)DTO.TUDelft.NL wrote: > > > >>David Marcus schreef: > >> > >>>Han.deBruijn(a)DTO.TUDelft.NL wrote: > >>> > >>>>David Marcus schreef: > >>>> > >>>>>Han de Bruijn wrote: > >>>>> > >>>>>>I'm not interested in the question whether set theory is mathematically > >>>>>>inconsistent. What bothers me is whether it is _physically_ inconsistent > >>>>>>and I think - worse: I know - that it is. > >>>>> > >>>>>What does "physically inconsistent" mean? Wouldn't your comments be > >>>>>better posted to sci.physics? Most people in sci.math are (or at least > >>>>>think they are) discussing mathematics. > >>>> > >>>>ONE world or NO world. > >>> > >>>Sorry. No idea what you mean. Do you have anything to say about > >>>mathematics or would you prefer we all just ignore you? > >> > >>It would save me a lot of time if some people here start to ignore me. > > > > Does that mean you have nothing to say about mathematics? > > Sigh! Start digging into my website. I've said more about mathematics > than anybody else in 'sci.math'. > > Han de Bruijn About as much as JSH, perhaps.
From: Virgil on 16 Oct 2006 15:14 In article <290c1$45333e14$82a1e228$8972(a)news2.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Dik T. Winter wrote: > > > In article <1160857746.680029.319340(a)m7g2000cwm.googlegroups.com> > > Han.deBruijn(a)DTO.TUDelft.NL writes: > > > Virgil schreef: > > ... > > > > I do not object to the constraints of the mathematics of physics when > > > > doing physics, but why should I be so constrained when not doing > > > > physics? > > > > > > Because (empirical) physics is an absolute guarantee for consistency? > > > > Can you prove that? > > Is it possible to live in a (physical) world that is inconsistent? The consistency of the physical world did not guarantee the consistency of the Phlogiston theory of combustion. Being a physicist is not a guarantee of being right, or of being consistent. Every physical theory must be, at least in theory, falsifiable, so that none of them can be held to be infallibly consistent. HdB is conflating the consistency of the world with the infallibility of its observers. The former is granted, the latter denied.
From: Virgil on 16 Oct 2006 15:20 In article <1161001547.844210.170720(a)k70g2000cwa.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > > > Every edge must have its own label if they are to be referred to by > > label. > > Of course, but what I did is only to give an example how the edges and > their parts are inherited. For my proof I do not need to refer to every > single edge but only to count the shares. Once you start split up edge,s one might equally well split up paths to have uncountably many parts of each path for each edge. In counting one does not split things up but only counts them as wholes. > > > > How about L and R a labels for the left and right branches at the root > > node, LL and LR for the left and right branches at the left node and RL > > RR for the rightmost pair at the right node , > > then LLL, LLR; LRL, LRR; RLL, RLR; RRL, RRR for edges at the next level, > > and so on ad infinitum. > > > > That gives every edge in the entire tree a unique label by which it may > > be referenced. > > Yes, if necessary, one could do so. It is necessary to deal with whole edges, not mere fractions of them, so it is necessary to have a unique identity for each edge and for each path if one is to compare the set sizes.
From: Virgil on 16 Oct 2006 15:23 In article <1161001750.193680.276740(a)f16g2000cwb.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > > > In article <1160815134.774717.182680(a)f16g2000cwb.googlegroups.com>, > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > > Virgil schrieb: > > > > > > > In article <1160675140.906009.253460(a)i42g2000cwa.googlegroups.com>, > > > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > > > > > > > > > > > > > this does not imply > > > > > > > > > > > > there exists a single unary number M such that for every digit > > > > > > position N, M covers 0.111... to position N > > > > > > > > > > Why shouldn't it? > > > > > > > > In general > > > > "for all x there is a y such that f(x,y)" > > > > does not imply > > > > "there is a y such that for all x f(x,y)". > > > > > > > > To establish the latter requires proof over and above the former. > > > > > > I did not state that this be true in general, but it is true in a > > > special case, namely for the covering of linear sets of finite > > > elements. > > > > > > What does "covering of linear sets of finite elements" mean? > > The infinite set of naturals, as it exists in ZF and NBG, is a linear > > set of finite elements according to the usual meanings of "linear order" > > and "finite elements". > > Alas, it is not (actually) infinite. Alas, it is not (actually) anything less than infinite in ZF or NBG, whatever it may be in "Mueckenh"'s dreamworld.
From: Virgil on 16 Oct 2006 15:28
In article <1161002747.410436.56240(a)i3g2000cwc.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > > > In article <1160835084.478453.305880(a)m73g2000cwd.googlegroups.com>, > > mueckenh(a)rz.fh-augsburg.de wrote: > > > > > Virgil schrieb: > > > > > > > > > > I do not object to the constraints of the mathematics of physics when > > > > doing physics, but why should I be so constrained when not doing > > > > physics? > > > > > > Because whatever you are doing, you are doing something, and "doing" > > > means utilizing and applying physics. > > > > > > That may be a physicists view of the world, but by that same measure, > > whenever one is doing physics, what he is really doing is math, so that > > mathematicians should rule. > > I would say that physics (measuring reality and deriving the laws > ruling reality) and mathematics are nearly the same, at least they were > the same as long as mathematics was mathematical. Therefore both depend > on reality. But they do not "depend on reality" in the same way. What physics claims must stand up to the demands of physical validation, but what mathematics says only need stand up to the demands of mental validation, as it exists only in the mental world. |