# Lower and Upper Limits [duplicate]

I am writing a document about limits of functions. I need to use notation for the lower limit, which I have as the normal limit sign but with 'lim' underlined. I need the same for the upper limit with 'lim' overlined.

For the overlined I have tried to use

\overline{\lim_{x \to 0^{+}}}


but that overlines all of it, I just want it over the 'lim' part.

## marked as duplicate by GuM, Bernard, Stefan Pinnow, Mike Renfro, ebosiMay 30 '17 at 23:39

• Don't reinvent the wheel: it already exists in the amsmath package under the name of \varliminf. See my answer to this question for this symbol and a few others in the same style. (lim sup, direct and inverse limits). – Bernard May 30 '17 at 21:58
• @Bernard: Of course!! (;-) So, this question should probably be marked as a duplicate, shouldn’t it? – GuM May 30 '17 at 22:07
• @Gustavo Mezzetti: It's also my opinion. – Bernard May 30 '17 at 22:09
• @Bernard: Done. But probably, you have got a gold badge that allows you to bypass the vote. – GuM May 30 '17 at 22:12
• @Gustavo Mezzetti: I don't how to do that. I simply voted to close (which I rarely do). – Bernard May 30 '17 at 22:14

Not a notation I recognise, but

\documentclass{article}

\usepackage{amsmath}

\DeclareMathOperator*\lowlim{\underline{lim}}
\DeclareMathOperator*\uplim{\overline{lim}}

\begin{document}

$\lim_{x \to 0^{+}} \rightarrow \lowlim_{x \to 0^{+}} \rightarrow \uplim_{x \to 0^{+}}$

\end{document}

• Ah, thank you. It's not notation I particularly like, but I couldn't think of a better one. – JSharpee May 30 '17 at 19:53
• It's not my notation. I am reading a book by Kenneth Falconer. – JSharpee May 30 '17 at 19:56
• @JSharpee Sorry! I misunderstood your comment, I deleted earlier comment (I still don't like the notation much though:-) – David Carlisle May 30 '17 at 19:57
• Aha, that's ok. I don't either. Thank you for your help. – JSharpee May 30 '17 at 19:59
• @JSharpee: Speaking of better notations, of course you know that LaTeX has \liminf and \limsup, which yield “lim inf” and “lim sup”, respectively, don’t you? – GuM May 30 '17 at 22:01

Oddly enough, this works:

$\overline{\lim}_{x \to 0^{+}}$


And it looks like this:

• that loses the mathop classification, so gets different spacing and the limit comes in subscript position not underneath as it does for \lim – David Carlisle May 30 '17 at 19:50
• Huh. That is weird and disturbing that it works. I will use the answer above if that's ok. Thanks though. – JSharpee May 30 '17 at 19:51