Timeline for Is asymptotic growth bound on a sequence equivalent to an asymptotic growth bound on its partial sum?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 11, 2020 at 21:56 | comment | added | Iosif Pinelis | Instead of the plain quantification over all $n$, the original question had $o(\cdot)$ asymptotics, which of course involves a $\forall\exists\forall$-type quantification. | |
| May 11, 2020 at 21:41 | comment | added | Gerhard Paseman | It looks like I was thinking upper bounds, not asymptotics. You are right about the definition of cn. I am wondering though if you need a quantification over all n in your statement. Gerhard "Thanks For Your Checking In". Paseman, 2020.05.11. | |
| May 11, 2020 at 21:36 | comment | added | Iosif Pinelis | @GerhardPaseman : It seems to me everything is correct there. E.g., if $a_k\equiv1$ and $b_n\equiv n^2$, then we take $c_n:=na_n=n$, and the equivalence $\iff$ holds. If $a_k\equiv1$ and $b_n\equiv n$, then we take $c_n:=a_n=1$, and the equivalence $\iff$ again holds. How do you get a complementary result? | |
| May 11, 2020 at 20:20 | comment | added | Gerhard Paseman | For the yes version above, it looks like cn is defined to give the complementary result. Gerhard "Would Like Some Further Explanation" Paseman, 2020.05.11. | |
| May 11, 2020 at 20:10 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |