On 21 Nov., 16:54, William Hughes <wpihug...@gmail.com> wrote: > On Nov 21, 11:37 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 21 Nov., 16:24, William Hughes <wpihug...@gmail.com> wrote: > > > > Your basic problem remains. You continue to talk > > > about "the" limit as if there was only one. > > > The real sequence has a limit. And if you dislike infinity as an > > improper limit, then take the reciprocals. They have *the* limit 0. > > Correct. Note that this limit is a real number. > > > This sequence is independent of anything else but its terms or its > > definition. > > > Set theory shows that *this sequence* has a limit without indices on > > You do not define *this sequence*.
This is exactly the same sequence. There is nothing further to define.
> If you mean the sequence of real > numbers you are incorrect.
I mean just this sequence of real numbers. And I am correct. Set theory does not leave any digit left of the decimal point in the limit.
> Set theory does say that there is > a limit of the set of digits to the left of the decimal place. > This limit is a set.
And this limit excludes the existence of any digit, which implies that there is no digit. > > > the left hand side, and hence has another limit (< 1) or no limit. > > The limit is {}. {} is not a real number. {} does not have a > reciprocal
But the numbers allowed by an empty set of decimal left to the point has a reciprocal, namely a value larger than 1. > > Two different limits which are not the same.
But one of the limits excludes the other one. And that is a contradiction.
You can also conclude that two different calculations of the same stuff may lead to two different results because the calculations are different. But mathematics does not tolerate that. That would kill math.
