Why can no one in sci.math understand my simple point?
in [Logic]
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From: |-|ercules on 15 Jun 2010 16:49 Snipping an argument doesn't disprove it Daryl. Try to address my point here. -------------------REPOSTED------------------- Cantor shows that 'any list is incomplete' By producing a NEW SEQUENCE of digits. Like so... 123 456 789 Diag = 159 Anti-diag = 260 Where are you getting a '260' when >the list of computable reals contain every digit of ALL possible infinite >sequences (3) Herc
From: Virgil on 15 Jun 2010 16:52 In article <4b892c9b-5125-46b6-8136-4178f0acac65(a)b35g2000yqi.googlegroups.com>, WM <mueckenh(a)rz.fh-augsburg.de> wrote: > On 15 Jun., 16:17, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > > > In this sense, the antidiagonal of the list of all computable reals > > is definable (but not computable). > > That is nonsense. To define means to let someone know the defined. If > he knows it, then he can compute it. There are undecidable propositions in mathematics, so if P is one of them then "x = 1 if P is true otherwise x = 0" defines an uncomputable number.
From: |-|ercules on 15 Jun 2010 16:57 "Virgil" <Virgil(a)home.esc> wrote ... > In article > <4b892c9b-5125-46b6-8136-4178f0acac65(a)b35g2000yqi.googlegroups.com>, > WM <mueckenh(a)rz.fh-augsburg.de> wrote: > >> On 15 Jun., 16:17, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: >> >> > In this sense, the antidiagonal of the list of all computable reals >> > is definable (but not computable). >> >> That is nonsense. To define means to let someone know the defined. If >> he knows it, then he can compute it. > > There are undecidable propositions in mathematics, so if P is one of > them then "x = 1 if P is true otherwise x = 0" defines an uncomputable > number. HAHAHA typical mathematicians' drivel about uncomputablity. Herc
From: Aatu Koskensilta on 15 Jun 2010 16:57 Virgil <Virgil(a)home.esc> writes: > There are undecidable propositions in mathematics, so if P is one of > them then "x = 1 if P is true otherwise x = 0" defines an uncomputable > number. Not in classical mathematics. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Virgil on 15 Jun 2010 17:02
In article <9f836f13-1633-45e1-a4ba-1d92b0953726(a)z8g2000yqz.googlegroups.com>, WM <mueckenh(a)rz.fh-augsburg.de> wrote: > On 15 Jun., 16:18, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > > Peter Webb says... > > > > >"WM" <mueck...(a)rz.fh-augsburg.de> wrote in message > > >news:62ae795b-1d43-4e1f-8633-e5e2475851aa(a)x21g2000yqa.googlegroups.com... > > >> On 15 Jun., 12:26, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > > > > >>> (B) There exists a real number r, > > >>> Forall computable reals r', > > >>> there exists a natural number n > > >>> such that r' and r disagree at the nth decimal place. > > > > >> In what form does r exist, unless it is computable too? > > > > >Of course its computable. > > > > No, it's computable *relative* to the list of all computable reals. > > But that list is not computable. > > That is nonsense! Only in WM's world. It makes perfectly good sense everywhere else. > > The list of all definitions is possible and obviously contains all > definitions of real numbers. That claim has been disproved, at least in standard mathematics, many times. What WM does in his own tiny world is of no consequence, except to his poor captive students. As well as the definitions of as many uncomputable numbers. For any undecidable proposition ,P, the number defined by "if P then x else y", where x and y are computable numbers and not equal, defines an uncomputable number. |