\usepackage{mathtools}
\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
The command \ceil will do; if called as \ceil*{x} it will add \left and \right; you can also call it as
\ceil[\big]{x} \ceil[\Big]{x} \ceil[\bigg]{x} \ceil[\Bigg]{x}
to state explicitly the size of the delimiters.
Answer from egreg on Stack Exchange\usepackage{mathtools}
\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
The command \ceil will do; if called as \ceil*{x} it will add \left and \right; you can also call it as
\ceil[\big]{x} \ceil[\Big]{x} \ceil[\bigg]{x} \ceil[\Bigg]{x}
to state explicitly the size of the delimiters.
Here is a simple xparse implementation of \ceil, similar to that provided by mathtools' \DeclarePairedDelimiter:
\documentclass{article}
\usepackage{xparse}% http://ctan.org/pkg/xparse
\NewDocumentCommand{\ceil}{s O{} m}{%
\IfBooleanTF{#1} % starred
{\left\lceil#3\right\rceil} % \ceil*[..]{..}
{#2\lceil#3#2\rceil} % \ceil[..]{..}
}
\begin{document}
\[\ceil[\big]{x} \quad \ceil[\Big]{x} \quad \ceil[\bigg]{x} \quad \ceil[\Bigg]{x} \quad \ceil*[\big]{\frac{1}{2}}\]
\end{document}
The optional argument is ignored in the starred version of \ceil*[..]{..}.
Using \DeclarePairedDelimiter from mathtools, you could define macros \ceil and \floor, which will scale the delimiters properly (if starred):
\documentclass{minimal}
\usepackage{mathtools}
\DeclarePairedDelimiter\ceil{\lceil}{\rceil}
\DeclarePairedDelimiter\floor{\lfloor}{\rfloor}
\begin{document}
\begin{equation*}
\floor*{\frac{x}{2}} \leq \frac{x}{2} \leq \ceil*{\frac{x}{2}}
\end{equation*}
\end{document}
Result:
You can define your own macro via the
\defcommand anywhere in your document. For example\def\lc{\left\lceil} \def\rc{\right\rceil}and then just write
\lc x \rc.Or you use the
\providecommandin the preamble, e.g.\providecommand{\myceil}[1]{\left \lceil #1 \right \rceil }to simply use
\myceil{x}in your document.- Use an editor, like vim, that allows for defining shortcuts for quick and efficient editing.
- And, finally, don't forget about readability of your tex document. Check out this thread for some instructive comments on how to write efficient and readable tex math docs.
Your function scales both input $x$ and output $y$ up by a factor of $100$:
$$
\lfloor 100 x \rfloor = 100y,
$$
i.e. if we define these scaled coordinates $X = 100x$ and $Y = 100y$, then the equation relating inputs to outputs looks like
$$
\lfloor X \rfloor = Y,
$$
which you can think of the prototype of the relationship between the variables. Putting all the transformations in one diagram looks like
$$
x \to X \to Y \leftarrow y,
$$
so the only way to build the composition $x \to y$ is to invert that last arrow $Y \leftarrow y$ to produce $Y \to y$, namely to divide by the scaling factor, hence we introduce fractions.
As always, we can hide the fraction inside of a definition, which doesn't change the fact that we're dividing by the scaling factor, but cosmetically, it might look nicer. We could, for instance, for any $p > 0$, define a rounding function with precision $\frac1p$ by $$ \operatorname{floor}_p(x) = \frac1p \lfloor p x \rfloor $$ that has the property that $\operatorname{floor}_p(x) = y$ for all $y \leq x \leq y + \frac1p$. With this notation, your example would look like $$ \operatorname{floor}_{100}(2.4783) = 2.47. $$
You are asking about truncation.
In the linked Wikipedia article, the notation is as follows.
Given a number $ x\in \mathbb {R}_+ $ to be truncated
and $n\in \mathbb {N} _{0}$, the number of digits to be kept after the decimal point,
the truncated value of $x $ is $\operatorname {trunc} (x,n)={\dfrac {\lfloor 10^{n}\cdot x\rfloor }{10^{n}}}$.
You should read some guides (starter guides) for LaTeX and math (especially about the sizes). With the knowledge about them you could easily adapt to this (\bigg):
\documentclass{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{mathtools}
\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
\begin{document}
\begin{equation}
\ceil[\bigg]{\frac{\log{(1-P_{0})}}{\log{(1-p)}}}
\end{equation}
\end{document}
Very simple, you can work with the asterisk.
\documentclass{memoir}
\usepackage{amsmath,amsfonts,amssymb}
\usepackage{mathtools}
\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}
\begin{document}
\begin{align}
\ceil*{\frac{\log (1-P_{0})}{\log (1-p)}}
\end{align}
\end{document}
I also applied some minor improvements on log vs \log.
Please consider the manual http://www.ctan.org/pkg/mathtools .
Just for adding some informal tags: Kenneth Eugene Iverson floor ceiling notation.
The comprehensive symbol list (see comprehensive) at least lists similar symbols with two vertical lines provided by package nath.
\documentclass{article}
\usepackage{nath}
\begin{document}
\[ \lceil a \rceil \lfloor a \rfloor \]
\[ \lCeil a \rCeil \lFloor a \rFloor \] % nath
\end{document}
Result:
Here are two macros \Ceil{<contents>} and \Floor{<contents>} that will create the paired delimiters and adjust to the height of <contents>.
It's hard to build this out of existing symbols because the floor and ceiling symbols have subtle differences at different sizes. Notably, they have round line caps when small but square (butt) line caps when Big.
So these are built from scratch using TikZ. By default all line caps and line joins are round, but you can change these with an optional argument:
\Floor[line cap=butt, line join=miter]{A}
You can also use the optional argument for a variety of TikZ options including color, line style, thickness, etc. For example,
\Ceil[blue, densely dotted, text=red, line width=.9pt]{A}
would work.
Here is the code:
\documentclass{article}
\usepackage{tikz, amsmath}
\newcommand{\Ceil}[2][]{{}\mathrel{\tikz[baseline, anchor=base, line join=round, line cap=round, #1]{
\node[inner sep=2pt] at (0,0)(a){$#2\mathstrut$};
\draw([shift={(0,2.8pt)}]a.south west)--([shift={(0,-2pt)}]a.north west)--++(2pt,0);
\draw([shift={(-1.5pt,2.8pt)}]a.south west)--([shift={(-1.5pt,-.5pt)}]a.north west)--++(3.5pt,0);
\draw([shift={(0,2.8pt)}]a.south east)--([shift={(0,-2pt)}]a.north east)--++(-2pt,0);
\draw([shift={(1.5pt,2.8pt)}]a.south east)--([shift={(1.5pt,-.5pt)}]a.north east)--++(-3.5pt,0);
}}{}}
\newcommand{\Floor}[2][]{{}\mathrel{\tikz[baseline, anchor=base, line join=round, line cap=round, #1]{
\node[inner sep=2pt] at (0,0)(a){$#2\mathstrut$};
\draw([shift={(0,-2pt)}]a.north west)--([shift={(0,2.8pt)}]a.south west)--++(2pt,0);
\draw([shift={(-1.5pt,-2pt)}]a.north west)--([shift={(-1.5pt,1.3pt)}]a.south west)--++(3.5pt,0);
\draw([shift={(0,-2pt)}]a.north east)--([shift={(0,2.8pt)}]a.south east)--++(-2pt,0);
\draw([shift={(1.5pt,-2pt)}]a.north east)--([shift={(1.5pt,1.3pt)}]a.south east)--++(-3.5pt,0);
}}{}}
\begin{document}
\[
\lfloor a\rfloor\lfloor A\rfloor \left\lfloor\frac{a}{b}\right\rfloor\lceil a\rceil\lceil A\rceil\left\lceil\frac{a}{b}\right\rceil\qquad
\Floor{a}\Floor{A}\Floor{\dfrac{a}{b}}\Ceil{a}\Ceil{A}\Ceil{\dfrac{a}{b}}
\]
\end{document}