> On 8 Mar 2019, at 22:00, John Clark <johnkcl...@gmail.com> wrote:
>
> On Fri, Mar 8, 2019 at 5:05 AM Bruno Marchal <marc...@ulb.ac.be
> <mailto:marc...@ulb.ac.be>> wrote:
>
> > BB(8000) is stil an infinitesimal (so to speak) compared to
> f_epsilon_0(BB(8000)).
>
> I don't know what "f_epsilon_0" is but if its computable then BB[BB(8000)]
Good point. But now, using epsilon_0, which is the constructive ordinal
omega^(omega^(omega^(omega^…, or equivalently omega tetrated to omega
(tetration is the iteration of exponentiation, like exponentiation is the
iteration of multiplication, and multiplication is the iteration of addition).
You can iterate the application of BB epsilon_0 times, and actually, alpha
times for alpha any constructive ordinal.
If the problem is to name a large number, or just to point to a large number,
in all case the winner is the one who will be able to use the constructive
ordinal.
Now, as you don’t ask for a name (definite description, programs to build that
name) the question raised if you could not iterate BB on non constructive
ordinals, but that will make the pointing even more fuzzy and not well
definite. Continuing this process will lead to inconsistency, at to some
undecidable threshold.
Bruno
> would be a larger number than that because BB grows faster than any
> computable function.
>
> John K Clark
>
>
>
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