An uncountable countable set
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From: David R Tribble on 30 Oct 2006 18:13 Tony Orlow wrote: > Apparently you are not aware of my > position on the subject. Bijections alone do not prove equinumerosity > for infinite sets. Cardinality is a rough measure of equivalence class, > not a precise measure of the size of a set. In order to precisely > compare such infinite sets of values, one must measure over a common > infinite value range formulaically. Then we easily get that half the > naturals are even, and other pleasant, intuitive notions. Consider the bijection f(n) = n^2 + 2n - 1, for all natural n>1. Obviously, this bijects all n>1 in N to some n>1 in N. n |f(n) ---|---- 1 | 2 2 | 7 3 | 14 4 | 23 : | : Let's say that f maps from set N1 to set Nf. So now what does f say about the "formulaic measure comparison" of the sizes of sets N1 and Nf? How much "bigger" is N1 than Nf?
From: MoeBlee on 30 Oct 2006 19:23 Tony Orlow wrote: > Intuitionistic logicians reject that a false premise > implies anything. Name such an intuitionistic logician and the work in which this appears. Intutitionistic logic DOES have the principle For all formulas P, f -> P ('f', the 'falsehood' symbol is often a primitive of intuitionistic (and certain formulations of classical) logic). Youv'e got it wrong, shooting of your big mouth on that which you know nothing, as usual. MoeBlee
From: MoeBlee on 30 Oct 2006 19:34 Lester Zick wrote: > On Sun, 29 Oct 2006 20:45:57 -0500, David Marcus > <DavidMarcus(a)alumdotmit.edu> wrote: > > >Lester Zick wrote: > >> On Sun, 29 Oct 2006 15:11:48 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: > >> >Lester Zick wrote: > >> >> According to MoeBlee mathematical definitions require a "domain of > >> >> discourse" variable such as IN(x) and OUT(x). > >> > > >> >I think you've used this joke enough already. Why don't you come up with > >> >a new one? > >> > >> Mainly because everyone seems to want to ignore the point Moe raised > >> regarding mathematical definitions. It would seem either Moe is right > >> or Stephen (I think) drew an improper mathematical definition or Moe > >> is not right. > > > >Or, you misunderstood what Moe said. I would think that would be the > >heavy favorite. > > Gee how hard can it be to understand "card(x)=least ordinal(x) with > equinumerous(x)" where x represents the domain of discourse? Very hard, since it's gibberish. And it's not my formula. Please stop misprepresenting what I posted. Your mangled versions are not my own. What I posted was: card(x) = the least ordinal equinumerous with x. MoeBlee > I mean I > can appreciate it might be difficult to understand the validity of > such particular definitions but I don't agree the form itself which > Stephen didn't choose to employ is especially difficult to comprehend. > Quite possibly you just misunderstand what Moe said and prefer not to > consider the possibility that one of the two is wrong. No, you're just (intentionally, it seems) mangling what I posted. Please stop doing that. MoeBlee
From: MoeBlee on 30 Oct 2006 19:41 Tony Orlow wrote: > I just don't get it. But don't forget: ~v~~ It explains it all. MoeBlee
From: MoeBlee on 30 Oct 2006 19:44
Tony Orlow wrote: > Virgil wrote: > > And in any system compatible with ZF or NBG there aren't any others. > > When did I claim my ideas were consistent with those "theories"? I don't know. But you seem to like non-standard analysis, which comes from those theories, and is, as itself an axiomatized theory, a conservative extension of them. MoeBlee |