On Fri, Jan 23, 2015 at 10:15 PM, meekerdb <[email protected]> wrote:
> On 1/23/2015 8:16 AM, Jason Resch wrote: > > > > On Friday, January 23, 2015, John Clark <[email protected]> wrote: > > > > On Thu, Jan 22, 2015 at 4:46 PM, Jason Resch <[email protected]> > wrote > > > >>> >> Do we know that? Do we know that such a digit exists? > >> > >> > It follows from the axioms that there is a certain definite digit. > > > > They show you how to generate terms in a sequence and if you add up > enough of them you'd get the the 10^(10^(10^100))th decimal digit of pi; > but it assumes that there is no barrier that makes doing that impossible > and states that assumption with 3 little dots (...). I don't know for > certain but those 3 little dots *might* be saying something that is logical > nonsense, I do know for certain that the first mathematicians who used > those 3 little dots knew nothing about quantum mechanics or the > computational limit of the universe, and that gives me pause. > > > > What I explained is that if you think there is a largest number *that* is > what definitely leads to logical nonsense. > > Say there is a largest number N, such that N+1 is not a bigger number, but > is still N. That means N+0 = N+1. Now subtract N from both sides. > > > Why should subtraction of the biggest number not obey special rules, e.g. > Subtracting N from any normal number yields -N. Subtracting N from any Big > number yields zero. > I still don't know if that would escape the problems. Let's say M is the number right before the biggest number (or any "Big numbers"). Then using your rules you find that: M - (M+1) = 0 --- or is it -N? but (M - M) + 1 = 1 It might be possible to come up with axioms that allow you to have a biggest number that operates in a consistent way, but I think it would be very difficult, and probably not very useful. Nor do I see the point of hobbling a theory (supposedly about the infinite natural numbers) by declaring some aspects of that theory to be strictly off limits and beyond the possibility of discussion. Jason -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
