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*. If you mean the sequence of real numbers you are incorrect. 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.
> 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
Two different limits which are not the same. No reason for them to be the same. No contradiction.
