On 10 Dez., 16:35, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> > Before 1908 there was quite a lot of mathematics possible. > > Yes, and since than quite a lot of newer mathematics has been made available.
Most of it being rubbish.
> Moreover, before 1908 mathematicians did use concepts without actually > defining them, which is not so very good in my opinion.
Cantor gave a definition of set. What is the present definition? >
> > N need not exist as a set. If n is a natural number, then n + 1 is a > > natural numbers too. Why should sets be needed? > > Ok, so N is not a set. What is it?
N is a sequence of natural numbers.
> > There is not even one single infinite path! > > Eh? So there are no infinite paths in that tree?
In fact no, but every path that you believe in is also in the tree, i.e., you will not be able to miss a path in the tree. > > > But there is every path > > which you believe to be an infinite path!! Which one is missing in > > your opinion? Do you see that 1/3 is there? > > If there are no infinite paths in that tree, 1/3 is not in that tree.
1/3 does not exist as a path. But everything you can ask for will be found in the tree. Everything of that kind is in the tree.
> Otherwise 1/3 would be a rational with a denominator that is a power of > 2 (each finite path defines such a number). > > > What node of pi is missing in the tree constructed by a countable > > number of finite paths (not even as a limit but by the axiom of > > infinity)? > > By the axiom of infinity there *are* infinite paths in that tree. So your > statement that there are none is a direct contradiction of the axiom of > infinity.
Try to find something that exists in your opinion but that does not exist in the tree that I constructed.