> On 7 Mar 2019, at 15:04, John Clark <johnkcl...@gmail.com> wrote: > > On Thu, Mar 7, 2019 at 8:18 AM Bruno Marchal <marc...@ulb.ac.be > <mailto:marc...@ulb.ac.be>> wrote: > > > Usually, when asked to name a big number, we mean to provide a number that > > e can compute in a finite time (no matter how long). BB(8000) will be > > rejected, because it is not a definite description, or name, because BB is > > not computable. > > Assuming you're just using 2 symbols (like 0 and 1) there are (16001)^8000 > different 8000 state Turing Machines. And that is a very large number but a > finite one. And one of those machines makes the largest number of FINITE > operations before halting. And that number of operations is BB(8000). Even > theoretically, much less practically, you can never compute that number but > I have given a unique description of it, no other 8000 state Turing Machine > has that propertie.
Yes, sure BB(8000) is a precise well defined finite number. But it is no what logician and philosopher call a “name”, where the number should be computable in principle. My point is just a vocabulary point, and a way to remind a nice problem which I have used to illustrate some less known application of Cantor’s diagonal. A constructive one, in this case. Then even using BB, you should still use the diagonalization, as BB(8000) is stil an infinitesimal (so to speak) compared to f_epsilon_0(BB(8000)). Bruno > > John K Clark > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
