TITLE: What does this 'L' and upside down 'L' symbol mean?
QUESTION [6 upvotes]: I need help finding out what the following symbols are called and what they do. I searched up math symbols but couldn't find them anywhere near there.
$$\lceil{-3.14}\rceil=$$
$$\lfloor{-3.14}\rfloor=$$

REPLY [3 votes]: Related to the two mentioned functions, there is the perhaps less common 
$\text{Nearest integer function } \lfloor x\rceil$.
$$\lfloor 3.2\rceil=3\\
\lfloor 3.6\rceil=4\\
\lfloor -1.2\rceil=-1$$
The function is ambiguous at numbers of the form $r+\frac 1 2, r\in \bf Z$, and so some kind of note should be made when using this function, clarifying what's to be done in those cases.
Note that we can set
$$
\lfloor x\rceil_1=\left \lfloor x+\frac 1 2\right\rfloor\\
\\
\lfloor x\rceil_2=\left \lceil x-\frac 1 2\right\rceil\\
$$
The first one rounds half integers up, and the second rounds them down.