In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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.
It is a sequence of numerals in place value notation but of unknown base. > > > > 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 as 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.
Since you have failed to demonstrate that set theoretic limits are invalid, why bother bring up non-set-theoretic limits only to fail?
> They depend > on arbitrary assumptions and interpretations.
The Lim-Sup and Lim-Inf definitions depend only on the existence of a sequence of sets, which is what the Vase problem provides. And since those two are equal, their common value is, again by definition, THE limit.
And for a limit of a sequence of sets, there is no other limit definition that is acceptable.
At least not in standard mathematics rather than WM's WMatheology.
> Mathematics must yield > results that are independent of interpretations.
Your own alleged results are never independent of interpretation!
And your own interpretations of them are almost always wrong. > > > > 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.
Lets see WM name anyone other than himself (whose competency is at best dubious anyway) as a mathematician who claims it ever has been done.
To the best of my > knowledge no competent mathematician accepts ZFC.
Z and F did.
And there is no evidence that WM is able to determine whether mathematicians are competent or not, since he is clearly not one of them. --