
Re: Why do we need those real nonconstructible numbers?
Posted:
Nov 9, 2017 1:54 AM


Am Mittwoch, 8. November 2017 22:55:27 UTC+1 schrieb burs...@gmail.com: > Except that the reals are uncountable. > This statement is based on a theory that violates logic and that violates mathematics. Mathematics proves
For all n in N: f(n) = {n, n+1, n+2, ...} > 10 ==> lim f(n) =/= 0
Set theor< requires li9m f(b) = 0.
The violation of logic is: There is a countable model of axioms VII and IV.
Axiom VII. The domain contains at least a set Z which contains the nullset as an element and is such that each of its elements a is related to another element of the form {a}, or which with each of its elements a contains also the related set {a} as an element.
Axiom IV. Every set T is related to a second set ?(T) (the '"power set" of T), which contains all subsets of T and only those as elements.
A model of a theory is a structure that satisfies the sentences of that theory, in particular its axioms.
Regards, WM

