In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 27 Nov., 08:41, Virgil <vir...@ligriv.com> wrote: > > In article > > <aaa8416f-f069-4525-9261-406792ffb...@u9g2000vbm.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 26 Nov., 20:55, Virgil <vir...@ligriv.com> wrote: > > > > > > > There are not different topologies involved when calculating sets of > > > > > digits of analytical limits. Nevertheless even you seem to be capable > > > > > of recognizing that set theory is not suitable for calculating limits > > > > > of analysis. > > > > > > While "different topologies" may be overstating the case, differing > > > > situations is not. > > > > > > WM compares a sequence of supposedly real numbers and a sequence of sets > > > > of digit positions, and says that because the limits of such different > > > > sequences can be different that mathematics has failed. > > > > > You have not yet understood. I compare the analytical limit of a > > > sequence of digits positions and the set theoretic limit of the same > > > sequence of digit positions. > > > > I understand that you compare apples to oranges and are unhappy to find > > they are different. > > > > > > > > > The analytical limit is obtained via (x --> oo) ==> (logx --> oo) from > > > the limit of the sequence of real numbers, but does that invalidate > > > the analytical mathod? > > > > Anyone who needs "(x --> oo) ==> (logx --> oo)" to compute the > > analytical limit of WM's sequence of reals > > Again you misunderstand. This relation is not needed to compute the > analytical limit of reals but to compute the set of indexed digits > left to the decimal point, or, as you call it, the limit of the > sequence of sets of positions left of the radix point.
Curious that no one but WM needs it for that purpose. And no one is looking for the sets of all such positions but only the sets representing non-zero digits, from which sequence every digit position is eventually excluded. > > > > > But however that limit is reached, it has nothing to do with the limit > > of the sequence of sets of positions left of the radix point having > > non-zero values, which limit is the empty set. > > The set of indexed digits left to the decimal point, or, as you call > it, the limit of the sequence of sets of positions left of the radix > point, is not empty - according to analysis.
The relevant digit positions to the left of the radix point are precisely those which contain non-zero digits, and every digit position eventually and permanently ceases to be one of those, so the limit contains no digit positions at all. > > According to set theory the limit set is empty. This is a > contradiction of analysis and set theory.
Not outside of Wolkenmuekenheim.
Outside of Wolkenmuekenheim every digit position to the left of the radix point eventually becomes occupied with a zero digit which will thereafter remain unchanged.
Thus the set of such digit positions to which this does NOT happen is empty.
It is amazing how careful WM is to close his eyes and mind to anything he does not wish to understand. --