4
$\begingroup$

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.

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

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

$\endgroup$
  • 5
    $\begingroup$ Try Detexify. $\endgroup$ – lhf Nov 3 '15 at 10:22
9
$\begingroup$

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

$\endgroup$
  • $\begingroup$ Ohhh! Thanks so much $\endgroup$ – Xirol Nov 3 '15 at 9:56
5
$\begingroup$

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

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

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

$\endgroup$
  • 3
    $\begingroup$ For completeness, there is also the Nearest Integer function: $\lfloor x \rceil$. $\endgroup$ – YoTengoUnLCD Dec 22 '15 at 22:04
  • $\begingroup$ @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. $\endgroup$ – BLAZE Dec 22 '15 at 22:09
  • 1
    $\begingroup$ Done! Thanks for the suggestion :-). $\endgroup$ – YoTengoUnLCD Dec 22 '15 at 22:20
3
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.