I just had a weird thought
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From: Charlie-Boo on 11 May 2010 15:06 On May 11, 2:50 pm, John Jones <jonescard...(a)btinternet.com> wrote: > taffer wrote: > > I just had a weird thought. It actually left me confused about what is > > mathematical, and what is physical. The statement was: > > > "Every finite set can be generated by adding one element at a time, > > starting from nothing". > > > This seems to be true. But then (and this is what confused me) I > > wondered, is that a mathematical statement? If so, would there not be > > a formal mathematical theorem expressing the statement? Or if it's a > > definition, a formal mathematical definition? Or maybe it's not a > > mathematical statement after all? > > What mystifies me is how you, and other mathematicians, seem to think > that adding one element at a time is one thing, and a new set is another > thing AND that they are both the same thing. In CBL it's M~N where M and N range over programs, meaning that M and N are functionally the same. It is defined in terms of the primitive # where M#f(I) expresses that M calculates function f, as (eA)M#A + N#A. M=N is defined as (eA)A#M + A#N so it's more primitive than equality. Reversing the definition of equality produces some interesting relations. Above it create the relation of two programs being functionally equivalent. It also produces the assertion that the universal set is recursively enumerable. TRUE(x) + P(I) => P(x) : Partially solvable => Recursively Enumerable EQ(I,J) + P(x) => P(I) : Recursively Enumerable => Partially Solvable Since TRUE(x) and EQ(I,J) are axioms in computer programming, r.e. = partially solvable, although people define them to be the same thing. C-B
From: Aatu Koskensilta on 11 May 2010 17:38 Charlie-Boo <shymathguy(a)gmail.com> writes: > On May 11, 2:04�pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > >> You are neither a Harvard grad student nor an MIT professor, > > How do you know? He knows. How do I know? I am a news poster. Oh, I still do believe in God, old man. I believe in God and Mercy and all that. But the dead are happier dead. They don't miss much here, poor devils. Them. And there. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 11 May 2010 17:39 Charlie-Boo <shymathguy(a)gmail.com> writes: > Since TRUE(x) and EQ(I,J) are axioms in computer programming, r.e. = > partially solvable, although people define them to be the same thing. No they don't. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 11 May 2010 22:02 "Jesse F. Hughes" <jesse(a)phiwumbda.org> writes: > I suppose I could be wrong, but I'm pretty sure that Aatu is neither > of a Harvard grad student nor an MIT professor. Uncanny. How could you possibly know these things? > It happens. Perhaps. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Nam Nguyen on 12 May 2010 02:10
Charlie-Boo wrote: > On May 11, 9:07 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: >> It's a mathematical >> triviality. That sounds like AK's writing all right. > > So? Do you forget that the most trivial of matters (FOM - FLT - > Arithmetic) have been debated for centuries and that problems trivial > to state can be massively difficult to solve? I could be wrong of course but it might have been the case he indeed forgot. > > Or are you just trying to be arrogant? Good question. But I think being genuinely arrogant is different from being loyal to and defending a regime that is passing. (A reasoning regime that is). I think he's just defending a regime in its waning days. > > (You used to be one of the rebels...) Then how come I've never seen him among my comrades in reasoning- arms, fighting against the Platonic Troops or the Godelian Guards? (So to speak of course.) |