In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 8 Apr., 19:13, Dan <dan.ms.ch...@gmail.com> wrote: > > > I use it as it is in order to contradict it. > > > > Should you contradict something, you can't use the contradicted thing > > as an argument to support something else . > > The contradiction has the same character as the famous proof that > sqrt(2) is not rational. It is assumed to be rational > > Here I assume that actual infinity exists. The result is > uncountability, i.e., the existence of a set that has uncountably many > different elements (elements that can be distinguiushed by infinite > sequences of digits or bits). But the Binary Tree shows that it is > impossible to distinguish uncountable many reals.
> > > > Every time you draw a line , you make "finished infinity" . > > That is not the case, since there is no finished infinity.
There is in geometry. If WM wants to exile geometry from mathematics, as well as any sane form of set theory, he is not going to have much mathematics left.
> But it is > in vain to discuss this by means of analogies and generalities. Try to > distinguish more than countably many infinite paths in the Binary > Tree. You will fail.
Then show me a surjection from |N to the set of paths of a CIBT!
I, and many many others, can prove both an injection and also the impossibility of a surjection from |N to the set of paths, so that the set of paths in a CIBT satisfies any reasonable definition of having "more" members than |N. > > > > The same goes for you and Set Theory .Can you imagine a world where > > there never was any 'Set Theory' for you to rant about?How would you > > get attention? > > I have done a lot of different things before. But I must confess that > set theory is the most interesting one, in particular the > psychological aspect that so many intelligent and bright people could > fall victims to it.
That only marks them as being both brighter and more intelligent than WM.
WM has many claims re set theory, but has not managed to provide supporting arguments for those claims that are any saner than the ones he objects to. --