"Virgil" <Virgil@home.esc> wrote > In article > <email@example.com>, > WM <firstname.lastname@example.org> wrote: > >> Pi is constructable and computable and definable, because there is a >> finite rule (in fact there are many) to find each digit desired. But >> as there are only countably many finite rules, there cannot be more >> defined numbers. > > If there are countably many rules then there are uncountably many lists > of rules capable of generating a number. > > > > > >> Therefore matheologicians have created undefinable >> "numbers". > > WM mistakes the issue. > > In pure mathematics, like in games, one has a set of rules to follow. > Differing sets of rules generate differing systems only some of which > are of much mathematical interest. > > The systems of rules we chose to use need not be subject to the > constraints that the system of rules that WM choses to play by are > subject to. > > For example, in FOL+ZFC, a commonly used system of rules which WM doe > not care for, all sorts of things are legitimate that none of WM's > systems of rules will allow. > > WM tries to force everyone to play only by his rules, but most of us > find his system of rules dead boring and of little or no mathematical > interest. > > Fortunately, outside of those classrooms in which his poor students are > compelled to play by his rules, he has no power to impose those rules on > anyone.
Unfortunately your last paragraph is speculation and your superinfinity rules are full of contradictions.
You show this example as Cantor's method
123 456 789
Diag = 159 AntiDiag = 260
But this method miserably fails on the computable set of reals, THERE IS NO new sequence like 260 in this example.
Why don't you rework Cantor's proof to define ALL anti-diagonals instead of 1 particular anti-diagonal?
Then the flaw in your method is obvious.
CONSTRUCT a new real
An AD(n) =/= L(n,n)
PROVE that this real is not on the list
An AD(n) =/= L(n,n)
[ An AD(n) =/= L(n,n) -> An AD(n) =/= L(n,n) ] -> Superinfinity
That is literally Cantor's diagonal proof of higher cardinalities.
Cantor's powerset proof is more ridiculous, no box contains the box numbers that don't contain their own box number -> Superinfinity
WM is entirely correct. You are a blind lost soul, a sacrificial Virgin.
What you call interesting or "paradise" we call ridiculous.