On 26 Mai, 04:07, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > In article <15af9b47-eac6-4d22-8720-0d6e7ebba...@e21g2000yqb.googlegroups.com> WM <mueck...@rz.fh-augsburg.de> writes: > > The problem boils down to the following: > > > > En Am: m =< n <==> Am En m =< n [*] > > En Am: m =< n ==> Am En m =< n [**] > > > > You know: Classical logic was obtained from finite sets ... > > Show me a finite set that obeys [**] but not [*]. > > The above is not contested: [**] implies > [*].
I said: For complete linear sets [*] is true. You said [*] is not true, but [**] is true. Weyl said: Classical logic was obtained from finite sets. Therefore I asked you: Show me a linear complete finite set, that makes your claim [**] right and my claim [*] wrong.
This is so simple that it should be understandable even for someone who is not "very deep in logic".
> What is contested is that: > En Am: m =< n <== Am En m =< n [***] > implies [*]. And *that* is the form you do use.
No. I do not use the implication only, I use the full equivalence. Of course the equivalence includes the implication [***] as well as the implication [**]
There is a trivial finite > counter-example. Take three dice where on each of the sides one of the > numbers one to nine is printed (some of them repeated). Say the set is {d1, > d2, d3}. Define di < dj when the probability to throw a higher number with > dj than with di is larger than to 1/2. (I would submit that all this is > quite physical.) There is a set of three dice such that d1 < d2, d2 < d3 and > d3 < d1. > > And so we have: > Am En d_m < d_n (d1 < d2 < d3 < d1) > but not > En Am d_m < d_n (there is no best die).
Of course there is no best die. Therefore this set is not linear. Every finite set of natural numbers has a "best" number.
Why do you bother with such nonsense examples? But the answer is easy: Because you have no other examples. _____________________
> Doesn't it bother you that he gets letters from > other mathematicians in Germany complaining > about it, and that he is proud about that fact?
I have never got a letter from a mathematician complaining about that. I would never publish a letter of my private correspondence without consent of the correspondent. My university of applied sciences got a letter from a greasy informer who may be whatever but certainly is not a mathematician.
> Do you not think that it might lower the value of other > degrees in Germany as well?
But you think it would increase this value if I taught, as you propose, that the sum of all natural numbers can be zero? Or if I taught, contrary to fact, Cantor's claim that a real number is the limit of its finite initial segments but all real numbers are not the limits of all their finite initial segments?
