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Dec 8, 2023 at 1:13 comment added LSpice @WillieWong, re, oh, I see! I was focussed on the answer, and missed the comment.
Dec 7, 2023 at 23:07 comment added Willie Wong @LSpice: Steven's wish (about advanced texts), but he is the post author so always gets notified. You were pinged also because of unordered infinite sums.
Dec 7, 2023 at 16:14 comment added LSpice @WillieWong, re, which witch wished which wicked wish? That is to say, whose wish?
Dec 7, 2023 at 3:01 comment added Willie Wong Your wish (wasn't) my command. And yes, unordered infinite sums are dealt with too. @LSpice
Nov 11, 2021 at 2:21 comment added LSpice Another example: the unordered sum $\sum_{x \in S} f(x)$ as a limit over the net of finite subsets $\lim_{F \subseteq S} \sum_{x \in F} f(x)$.
Jul 17, 2017 at 18:43 comment added Todd Trimble Steven -- oh of course. But if one should be teaching topology, it's a good example to keep in mind!
Jul 17, 2017 at 18:35 comment added Steven Gubkin @ToddTrimble Me either! Although that is a bit more structure than the typical calculus class probably wants to dive into. I am surprised that I have not seen this definition as part of more advanced texts though.
Jul 17, 2017 at 11:53 comment added Todd Trimble I don't think it's occurred to me before now that actually the Riemann integral is more naturally viewed as a limit of a net than as a limit of a sequence.
Aug 27, 2012 at 13:00 history made wiki Post Made Community Wiki by Steven Gubkin
Aug 27, 2012 at 9:28 comment added Wadim Zudilin +1 for your CW comment: I really forgot about this natural option.
Aug 26, 2012 at 15:33 history answered Steven Gubkin CC BY-SA 3.0