What does this 'L' and upside down 'L' symbol mean? 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.
$$\lceil{-3.14}\rceil=$$
$$\lfloor{-3.14}\rfloor=$$
 A: The notation $\lfloor x \rfloor$ (known as ‘the floor function’) denotes the largest integer less than or equal to $x \in \mathbb{R}$. Examples include $\lfloor7\rfloor$ = $7$, $\lfloor2.5\rfloor$ = $2$, $\lfloor\pi\rfloor$= $3$ and  $\lfloor−2.5\rfloor$ = $-3$.
The notation $\lceil x \rceil$ (known as ‘the ceiling function’) denotes the smallest integer greater than or equal to $x \in \mathbb{R}$. So using the same examples as before $\lceil7\rceil$ = $7$, $\lceil2.5\rceil$ = $3$, $\lceil\pi\rceil$= $4$ and  $\lceil−2.5\rceil$ = $-2$.   
So for your examples
$$\lceil{-3.14}\rceil=-3$$
$$\lfloor{-3.14}\rfloor=-4$$
A: 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.
A: They are ceil and floor values, that is they are the closest integers one  below and one above respectively , see link.
