In article <d5e9dd71-084a-4257-9f1e-70f9b486043d@g16g2000yqi.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 16 Okt., 01:52, Virgil <vir...@ligriv.com> wrote: > > In article > > <333f9aa0-baae-4277-8a8c-9ceb9efb5...@v28g2000vby.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > Where can I find that? Where is the proof that the sequences > > > 1, 2, 3, ... > > > and > > > 1, 2, 3, ... > > > can have different limits? > > > > Among other times, when they exist in differently topologized spaces > > These sequences exist independently from any spaces. They are the > natural numbers. If spaces do not account for this fact, then the > spaces are useless. > > Regards, WM
But limits require definition, which in proper mathematics is usually done in topological terms, so the same sequence can have differing limit properties depending on the topological properties in which it finds itself.
