
Re: Endorsement of Wolfgang Mueckenheim from a serious mathematician
Posted:
Feb 1, 2013 3:12 AM


On 1 Feb., 06:01, forbisga...@gmail.com wrote: > On Thursday, January 31, 2013 8:55:12 AM UTC8, WM wrote: > > On 31 Jan., 15:27, forbisga...@gmail.com wrote: > > > > The rational 1/3 > > > > doesn't have a finite decimal expansion. None the less it is distinguishable > > > > from every rational other than 1/3 at some place in the expansion > > > > and only the infinite expansion can be calculated to be 1/3. > > > If you are so sure about that than you should be able to find out > > > whether 1/3 is among the paths that I have used to construct the > > > complete infinite Binary Tree. Does it in fact differ from the union > > > of all its finite initial segments > > > 0.01 > > > 0.0101 > > > 0.010101 > > > ... > > Yes it does, under the assumption that the continuation > of all of your initial segments is not the repeating sequence > [01]. If it is then I will
If you could determine it by nodes or digits, you need not make provisions. So you cannot determine by nodes whether 1/3 it there or not. QED.
There remains only a finite definition. But there are only conutably many.
If it is then I will give you the repeating sequence 0.[001] and it will not be among your finite initial segments unless you change your continuation at which point 0.[01] will not be in your set.
And if I append to every finite path every infinite tail that has a finite definition like 0.[001]? What will you choose then??? Nevertheles I will have used only countably many paths yet.
Regards, WM

