On 6/21/07, Taral <[EMAIL PROTECTED]> wrote:
On 6/21/07, Ian Kelly <[EMAIL PROTECTED]> wrote:
> What do you mean by "computable natural number"? In the sense meant
> by "computable real number", all natural numbers are trivially
> computable. I can envision that a natural number might be called
> computable if it is the Godel number of a computable function or set,
> but that's not a usage I'm familiar with.
The busy beaver S() function, for example, is a canonical example of a
non-computable function yielding natural numbers. I call these
"non-computable natural numbers".
Seems like bad terminology to me, since the same numbers (whatever
they might be) are computable. I'm not sure what would be better.
Non-computable image, perhaps?
-root
