In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 27 Nov., 20:14, Virgil <vir...@ligriv.com> wrote: > > > > > 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. > > That is easy to explain. You are brain-washed such that you have > forgotten to do mathematics without completed infinity. Nevertheless, > it is not forbidden, I assume, to use analysis?
It certainly seems as if someone or something has forbidden WM to use it.
> > > According to set theory the limit set is empty. This is a > > > contradiction of analysis and set theory.
Analysis says nothing about the limit of the set of nonzero digits, but does say that the limit of the sequence of numbers involved is NOT A NUMBER. And being not a number need not have any digits at all. > > > 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. > > Sorry, not in set theory. Set theory proves that there is no digit > whatever in the limit left to the point.
We start with the infinite set of digits to the left of the decimal point, and while we change their values, at each step will still have an infinite set of digits However the sequence subsets of that original set having non-zero values has the empty set as its limit, as each digit position can be shown to eventually have value zero and keep value zero thereafter.
But of course, this is much to complicated o WM to sort out, so he keeps objecting to the obvious. > > It is amazing how careful WM is to close his eyes and mind to anything > > he does not wish to understand. > > Please try to opne your eyes to thing that you wish to understand. > > Regards, WM --