Cantor Confusion
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From: Lester Zick on 18 Nov 2006 13:35 On 17 Nov 2006 14:49:13 -0800, "David R Tribble" <david(a)tribble.com> wrote: >david petry schrieb: >>> Thinking about this question leads most of us to believe that there >>> is a core of mathematics which every such civilization will accept. >> > >mueckenh wrote: >>> without axioms, yes. For instance: I + I = II (after translating "+" >>> and "="). Therefore I call this an absolute truth. >> > >David R Tribble wrote: >>> Which axioms are you using to describe the "+" and "=" operators? >> > >Lester Zick wrote: >> None. > >Then how can you know it is true? An interesting question at least for a change. Problem is you don't advance knowledge of what's true by canonizing assumptions of truth in axioms. To find truth you need to find mechanically irreducible principles of what is universally false and truth is what's left over. I approach the problem in mechanical terms tautologically, by observing only differences can be true because there can be nothing "different from differences". The idea of "different from differences" or the "contradiction of contradiction" is self contradictory which I take to be false in exhaustive mechanical terms. Consequently what's left over in tautological terms is "contradiction" or "differences" so that must perforce be true and be true of everything in universal terms. >In fact, it looks wrong to me. I think it should be I + I = I. But >perhaps I have a different implicit understanding of "+" and "=". >What do your "+" and "=" mean? Well if you approach the problem from the perspective of finite tautological regression to self contradictory alternatives then "=" and "+" and all other things simply represent various compoundings of differences. "=" doesn't just apply to everything willy-nilly. Does the "first" "=" the second? No of course not. "=" and "+" do not apply to ordinality they only apply to cardinality where differences between intervals are the same. In other words "+" = "- -" under certain mechanical restrictions. The Peano axioms and the suc( ) axiom simply assume "+" as the foundation of mathematics when in point of fact "-" represents the foundation of all things in universal mechanical terms including mathematics. Hell the Peano axioms and the suc( ) axiom can't even produce straight lines. At best they produce various straight line segments of equal unit length but there is no guarantee that those straight line segments align with one another on any straight line. Only Newton's differential calculus can produce straight lines through his method of drawing tangents to curves. And those straight lines can be further subdivided in equal terms through infinitesimal subdivision and conversely integrated. That's where we get our knowledge of what's true mathematically when it comes to the manipulation of differences in terms of one another. All we need to do is recognize the various kinds of differences involved and the properties of the various kinds of differences such as unequal differences or ordinality and equal differences or cardinality which determine the properties of operations on them such as commutivity and distributivity for mathematical purposes. In other words none of these things require mathematical canonization in the form of axioms and all are demonstrable in mechanical terms. Technically (there you go, Brian) the only "assumption" I make is that self contradiction is false. And everything else is derived from that. Otherwise we might just say something like "the self contradictory set is necessarily and universally empty and must necessarily remain so". However I think the point is nugatory regardless and we can be permitted the minor terminological assumption that self contradiction means false in every language possible. ~v~~
From: David Marcus on 18 Nov 2006 13:37 Lester Zick wrote: > What is it modern zen mathematikers do instead of thinking about the > truth of what they say? Sit around all day massaging their middle > legs? I mean really what is it they expect they get paid for? Proving theorems, of course. Fess up: you really knew that, didn't you? -- David Marcus
From: David Marcus on 18 Nov 2006 13:44 Lester Zick wrote: > I'm saying that you don't understand what a mathematical definition is > but nonetheless want to pretend you do. If a mathematical definition > were "just" an abbreviation as you claim you wouldn't have any way to > tell one mathematical definition from another. Why not? Suppose I make the following definitions. Let N denote the set of natural numbers. Let R denote the set of real numbers. Then I can tell N and R are different because their defintions are different. If I write 0.5 is not in N, then this means the same as 0.5 is not in the set of natural numbers. And, it means something different from 0.5 is not in R. -- David Marcus
From: David Marcus on 18 Nov 2006 14:25 Franziska Neugebauer wrote: > mueckenh(a)rz.fh-augsburg.de wrote: > > Franziska Neugebauer schrieb: > >> mueckenh(a)rz.fh-augsburg.de wrote: > >> > William Hughes schrieb: > >> >> Let he original matrix be A. > >> [...] > >> > 1 > >> > 12 > >> > 123 > >> > ... > >> > >> Something is missing here: > >> > >> 1uuu... > >> 12uu... > >> 123u... > >> ... > > > > No. > > Wrong. You have been discussing matrices. At least William Hughes did. > Are you both writing at cross purposes? WM is always writing at cross purposes to everyone! -- David Marcus
From: David Marcus on 18 Nov 2006 14:29
Franziska Neugebauer wrote: > mueckenh(a)rz.fh-augsburg.de wrote: > > > I used this suitable word because it allows to speak of lines, columns > > and diagonal. > > _Define_ what you mean! That would make it too simple! > I suspect you are speaking of matrices, lines, > columns and the like in default of a reasonable point of view. > > > If you don't like it, say triangle or structure. I > > propose to use "infinite triangle" in order to be clear and to show > > that your commentary below fails to show anything. Instead of "square" > > we should speak of "equilateral". So we have an Equilateral Infinite > > Triangle: EIT. > > Another misnomer. Cf. my posting in reply to David Marcus. > <45550ba7$0$97245$892e7fe2(a)authen.yellow.readfreenews.net> At least I defined what I meant. And, I never said "equilateral"! -- David Marcus |