# 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.

$$\lceil{-3.14}\rceil=$$

$$\lfloor{-3.14}\rfloor=$$

They are ceil and floor values, that is they are the closest integers one below and one above respectively , see link.

• Ohhh! Thanks so much Nov 3, 2015 at 9:56

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 $\lceil−2.5\rceil$ = $-2$.

$$\lceil{-3.14}\rceil=-3$$

$$\lfloor{-3.14}\rfloor=-4$$

• For completeness, there is also the Nearest Integer function: $\lfloor x \rceil$. Dec 22, 2015 at 22:04
• @YoTengoUnLCD Oh wow, I never heard of that one before; thanks for pointing it out :) Perhaps you should make this as an answer, and give some examples for it (maybe the same numerical figures as I used for comparison). It's still vaguely related to OP's question. Besides, I would like to see this function in action! Thank you. Dec 22, 2015 at 22:09
• Done! Thanks for the suggestion :-). Dec 22, 2015 at 22:20

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.