On 18 Jul., 00:55, Virgil <vir...@ligriv.com> wrote: > In article
> > Only if you interpret the real sequence > > 01 > > 0.1 > > 010.1 > > 01.01 > > 0101.01 > > 010.101 > > ... > > as I proposed > > That sequence of reals does not have a real limit.
It has the (improper) limit oo, because the reciporcals have the limit 0.
> Set theory does not determine any limit for that last sequnce, since it > is not a sequence of sets
It is a sequence of sets of indexed digits. It is only written with a point between some arbitrarily selected elements in order to veil the problem.
> > Although the results depend, as I have just shown, on the direction of > > reading? Europeans will get the limit 0, Arabians will get the limit > > oo. And Chines and Japanes, who read from top to bottom? What limit > > will they obtain? > > But s none of those limits, even if they were valid, are relevant to the > vase problem, why bring them up?
In order to show that set theoretical limits are invalid. They depend on arbitrary assumptions and interpretations. Mathematics must yield results that are independent of interpretations. > > To the best of my knowledge, no competent mathematician or logician now > claims to have derived a "P and not P" statement within either ZF or ZFC.
That depends on the interpretation of competent. To the best of my knowledge no competent mathematician accepts ZFC.