Definition talk:Limit Superior

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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 $\R \to \bar \R$,
$\ds \limsup_{x \mathop \to a} \map f x := \inf_{\delta > 0} \set {\sup_{\size {x - a} < \delta} \map f x : x \in \R}$

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

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

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