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Re: Mathelogy S 011
Posted:
May 21, 2012 10:10 PM
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On May 21, 10:38 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 21 Mai, 19:19, "dilettante" <n...@nonono.no> wrote:
> > Mathematicians and computer scientists should get busy defining as many
> > numbers as they can as quickly as possible. Some supercomputers should be
> > devoted to this task. I bet there is very little being done on this.
> > Probably there aren't any more numbers now than there were last Tuesday, and
> > that is just pathetic.
> This sound like a joke, but it is a serious problem. I am not able to
> define definability. But I am able to define what cannot be defined.
> Numbers with a Kolmogorov-complexity of 10^100 bits for instance (as
> the length of the smallest possible definition) do not exist.
OK. So in WM's matherealism, there exists an upper bound on the
Kolmogorov-complexity of a natural number, whereas in standard
theory (matheology), no such limit exists.
I have no problem with there being an upper bound on the natural
numbers that exist. One large number that appears in any known
proof is Graham's number, so I consider it harmless to have a
system in which no number larger than G exists. And in WM's
matherealism, there are many classical naturals between 1 and G
that aren't matherealistic naturals. One would be hardpressed to
find a known mathematical proof in which naturals with large
complexity occur.
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