Definition talk:Limit Superior

Renaming issues will come up and I'm not sure how to disambiguate and what to name the pages


 * $(1)$ Folland defines the concept for all for all sequences in $\bar{\R}$, bounded or not, in the obvious way. Is that a sub-entry of this one, or a super-entry, or seperate, or ... ?


 * $(2)$ Folland also defines the $\sup$ of functions $\R \to \bar{\R}$,


 * $\displaystyle \limsup_{x \to a} f(x) := \inf_{\delta > 0}\left\{ { \sup_{|x-a|<\delta} f(x) : x \in \R } \right \}$

I also don't know what to call this or where to put it. --GFauxPas (talk)


 * It's actually a more global issue than this. For example, Bolzano-Weierstrass hypotheses can be relaxed if a "convergent subsequence" includes a limit at $+\infty$ or $-\infty$. And so on. --GFauxPas (talk)


 * If there is a definition for Limit Superior in multiple contexts, then each one needs its own page for that concept. If they are similar enough, they can be transcluded into a master page. I don't have Folland, and I haven't gone down this route into Analysis for many years (and never went much further than graduate level) so I'd need to do research. --prime mover (talk) 17:01, 27 May 2018 (EDT)

Source Help
See: https://imgur.com/a/OXEX0QP

-- 19:13, 20 June 2019 (EDT)


 * Many thanks. --prime mover (talk) 01:51, 21 June 2019 (EDT)