Timeline for Generalized limits
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 5, 2019 at 21:28 | comment | added | Anixx | @LSpice as you can see it directly mentions the generalized limits. It was before this question posted. I do not know what topic can be related closer if we talk about limits of divergent series. | |
| Nov 5, 2019 at 21:03 | comment | added | LSpice | With all due respect, I think that advertising about it in questions to which it does not seem directly related doesn't belong here; but the voting on your answer shows that that might be a minority opinion. | |
| Nov 5, 2019 at 19:20 | comment | added | Anixx | @LSpice as an algebraist, what do you think about algebraic properties of the linked system? I posted a question about this here: math.stackexchange.com/questions/3390772/… | |
| Nov 5, 2019 at 17:01 | comment | added | LSpice | What I meant is that the natural projection $X^{\mathbb N} \to X^{\mathbb N}/c_0(X)$ is a reasonable, if not very interesting, kind of "generalised limit with generalised values", and, via the inclusion of constant sequences $X \hookrightarrow X^{\mathbb N}$, agrees with the usual limit on convergent sequences; but it seems likely it's not what @user76284 had in mind. (It's also not what you said! I just meant that some care needs to be taken when extending the admissible values of the limit.) | |
| Nov 5, 2019 at 14:45 | comment | added | Anixx | @LSpice can you please provide an example of what your concern can lead to. | |
| Nov 4, 2019 at 16:59 | comment | added | LSpice | One has to be very conservative extending the range of possible limits beyond the complex numbers, or else you could do something like taking the codomain to be the quotient of $X^{\mathbb N}$ by the ideal of sequences tending to $0$. (Of course you haven't done this, but what I mean is that it might be easy to sneak up accidentally on doing this by innocent-seeming steps.) | |
| Nov 4, 2019 at 12:47 | history | edited | Anixx | CC BY-SA 4.0 |
added 173 characters in body
|
| Nov 4, 2019 at 12:41 | history | answered | Anixx | CC BY-SA 4.0 |