
Re: Why do we need those real nonconstructible numbers?
Posted:
Nov 9, 2017 1:44 AM


Am Donnerstag, 9. November 2017 03:42:45 UTC+1 schrieb Jim Burns:
> There are more subsets of the natural numbers (uncountably > many) than there are definitions of _anything_ including > subsets of the natural numbers (at most countably many).
In order to prove that you need to contradict mathematics, namely the theorem:
For all n in N: f(n) = {n, n+1, n+2, ...} > 10 ==> lim f(n) =/= 0.
> Therefore, there are undefinable subsets of the natural > numbers.
The conclusion from an invalid premise. > > What was that sound? Was it the foundations of the > universe trembling?
Fortunately the real universe is not touched by matheology.
> No, it wasn't. The universe is fine, > it's just that there are some things we can't define.
passeth all reasonable. That's a parallel with other theology.
Regards, WM

