In article <250e1f42-8d35-42f0-969b-3f919b4ce5e4@c33g2000yqm.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 15 Jun., 22:52, Virgil <Vir...@home.esc> wrote: > > In article > > <4b892c9b-5125-46b6-8136-4178f0aca...@b35g2000yqi.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 15 Jun., 16:17, stevendaryl3...@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. > > 3 is a number. n is a number form. > 5 < 7 is an expression. m < n is the form of an expression. > f(n) = (1 if Goldbach is correct) is not a function and it is not > computable.
For a long time, g(n) = ( if FLT is true then 1 else 0) was unknown, but now it is known.
So unless WM can prove that Goldbach's conjcture will be forever undetermined, he cannot claim f(n) = (1 if Goldbach is correct, 0 otherwise) is not a function.
