+112 Sample Greek
\alpha • \beta • \gamma • \Gamma • \pi • \Pi • \phi • \Phi • \varphi • \mu
\(\alpha • \beta • \gamma • \Gamma • \pi • \Pi • \phi • \Phi • \varphi • \mu \)
Trigonometry
\cos() • \sin() • \tan()
\(\cos() • \sin() • \tan()\)
Lims
\lim_{x \to \infty} \exp(-x)=0
\(\lim_{x \to \infty} \exp(-x)=0\)
Sample B Mod
a \bmod b
\(a \bmod b\)
Sample P Mod
x \equiv a \pmod{b}
\(x \equiv a \pmod{b}\)
Subscripts and Superscripts
x^y • x^{y+z} • x_y • x_{y+z}
\(x^y • x^{y+z} • x_y • x_{y+z}\)
Fractions
\frac{1}{2} • \binom{1}{2} • ^3/_7
\(\frac{1}{2} • \binom{1}{2} • ^3/_7\)
Superscript Fractions
x^\frac{1}{2}
\(x^\frac{1}{2}\)
Square Roots
\sqrt{16} = 4
\(\sqrt{16} = 4\)
n-th Roots
\sqrt[3]{27} = 3
\(\sqrt[3]{27} = 3\)
Large Operations
\sum • \prod • \coprod • \bigoplus • \bigotimes • \bigodot • \bigcup • \bigcap • \biguplus • \bigsqcup • \bigvee • \bigwedge • \int • \oint • \iint • \iiint • \iiiint • \idotsint
\(\sum • \prod • \coprod • \bigoplus • \bigotimes • \bigodot • \bigcup • \bigcap • \biguplus • \bigsqcup • \bigvee • \bigwedge • \int • \oint • \iint • \iiint • \iiiint • \idotsint\)
Types of Brackets
(a) • [b] • \{c\} • |d| • \|e\| • \langle f \rangle • \lfloor g \rfloor • \lceil h \rceil • \ulcorner i \urcorner
\((a) • [b] • \{c\} • |d| • \|e\| • \langle f \rangle • \lfloor g \rfloor • \lceil h \rceil • \ulcorner i \urcorner\)
Sizes of Brackets
(1) • \big(2\big) • \Big(3\Big) • \bigg(4\bigg) • \Bigg(5\Bigg)
\((1) • \big(2\big) • \Big(3\Big) • \bigg(4\bigg) • \Bigg(5\Bigg)\)
Matrices
\begin{matrix}...
a &-b-& c \\
d &-e-& f \\
g &-h-& i
\end{matrix}
\(\begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix}\)
Dot Symbols
\cdots • \vdots • \ddots
\(\cdots • \vdots • \ddots\)
Arrays (can be programmed as tables)
\begin{array}{c|c}...
1-&-2 \\
\hline
3-&-4
\end{array}
\(\begin{array}{c|c} 1 & 2 \\ \hline 3 & 4 \end{array}\)
Text
Warning: When you don't include "\text{}" between text, they will not have any inputted spaces, but will have uneven spacing between the F's.
50 apples \times 100 apples = lots of apples^2 • 50 \text{ apples} \times 100 \text{ apples} = \text{lots of apples}^2
\(50 apples \times 100 apples = lots of apples^2 • 50 \text{ apples} \times 100 \text{ apples} = \text{lots of apples}^2\)
Text Formatting
\textrm{regular} • \textbf{bold} • \textit{italic} • \text{text}
\(\textrm{regular} • \textbf{bold} • \textit{italic} • \text{text}\)
Accents
a' • a'' • a''' • a'''' • \hat{a} • \bar{a} • \grave{a} • \acute{a} • \dot{a} • \ddot{a} • \not{a} • \mathring{a} • \overrightarrow{abc} • \overleftarrow{abc} • \overline{abc} • \check{a} • \breve{a} • \vec{a} • \dddot{a} • \ddddot{a} • \widehat{abc} • \widetilde{abc} • \stackrel\frown{abc} • \tilde{a} • \underline{a}
\(a' • a'' • a''' • a'''' • \hat{a} • \bar{a} • \grave{a} • \acute{a} • \dot{a} • \ddot{a} • \not{a} • \mathring{a} • \overrightarrow{abc} • \overleftarrow{abc} • \overline{abc} • \check{a} • \breve{a} • \vec{a} • \dddot{a} • \ddddot{a} • \widehat{abc} • \widetilde{abc} • \stackrel\frown{abc} • \tilde{a} • \underline{a}\)
Colors
{\color{red}c}{\color{orange}o}{\color{yellow}l}{\color{green}o}{\color{blue}r}{\color{purple}s}
\({\color{red}c}{\color{orange}o}{\color{yellow}l}{\color{green}o}{\color{blue}r}{\color{purple}s}\)
Large Operations In Use
\sum_{x=1}^5 x+1=20 • \prod_{x=1}^5 x+1=720 • \int_1^e ln(x)dx = 1 • \frac{d}{dx}sin(x) |_{x=\frac{\pi}{2}}
\(\sum_{x=1}^5 x+1=20 • \prod_{x=1}^5 x+1=720 • \int_1^e ln(x)dx = 1 • \frac{d}{dx}sin(x) |_{x=\frac{\pi}{2}}\)
If you want these to be more like what is on paper, do this code with "begin(split)" and "end(split)".
\begin{split}\
\sum_{x=1}^5.x+1=20.• \prod_{x=1}^5 x+1=720 • \int_1^e ln(x)dx = 1 • \frac{d}{dx}sin(x) |_{x=\frac{\pi}{2}}\
\end{split}\
\(\begin{split} \sum_{x=1}^5 x+1=20 • \prod_{x=1}^5 x+1=720 • \int_1^e ln(x)dx = 1 • \frac{d}{dx}sin(x) |_{x=\frac{\pi}{2}} \end{split}\)
If you want to learn more about LaTeX Formatting, visit this article from Wikibooks.
+112 Extra Lines
2\times2=4\\
4\times2=8
\(2\times2=4\\ 4\times2=8\)
Put a Symbol on Top of Another
\stackrel{?}{=} • \stackrel{\checkmark}{=}}
\(\stackrel{?}{=} • \stackrel{ \checkmark }{=}\)
Put a Symbol on the Bottom of Another
\underset{2}{4} • \underset{x \to \infty}{\lim}
Warning: The "\lim" command and its subscript text (like described above) styled this way below does not fix the text the way it's supposed to be.
\(\underset{2}{4} • \underset{x \to \infty}{\lim}\)
Braces for Grouping
z=\overbrace{ \underbrace{x}_text{real}+i \underbrace{y}_\text{imaginary} }^\text{complex number}
\(z=\overbrace{ \underbrace{x}_\text{real}+i \underbrace{y}_\text{imaginary} }^\text{complex number}\)
Complex Numbers
z=\overbrace{\underbrace{a}_\text{real}+\underbrace{b}_\text{imaginary}i}^\text{rectangular}\\\
z=\overbrace{\underbrace{r}_\text{real}\angle\underbrace{\theta}_\text{imaginary} \text{ or }.z=\underbrace{r}_\text{real}\underbrace{e^{\theta i}}_{imaginary}}^\text{polar}
\(z=\overbrace{\underbrace{a}_\text{real}+\underbrace{b}_\text{imaginary}i}^\text{rectangular}\\ z=\overbrace{\underbrace{r}_\text{real}\angle\underbrace{\theta}_\text{imaginary} \text{ or } z=\underbrace{r}_\text{real}\underbrace{e^{\theta i}}_{imaginary}}^\text{polar}\)
Arrows with Text
A \xleftarrow{\text{this way}} B \xrightarrow[\text{or this way}]C
\(A \xleftarrow{\text{this way}} B \xrightarrow[\text{or this way}] { } C\)
Align Text Against a Specific Symbol
\begin{align*}
f(x) &= (x+a)(x+b)\\
&= x^2 + (a+b)x+ab
\end{align*}
\(\begin{align*} f(x) &= (x+a)(x+b)\\ &= x^2 + (a+b)x+ab \end{align*}\)
Equal Sign and Other Similar Signs
< • > • = • \parallel • \nparallel • \leq • \geq • \doteq • \asymp • \bowtie • \ll • \gg • \equiv • \vdash • \dashv • \subset • \supset • \approx • \in • \ni • \subseteq • \supseteq • \cong • \smile • \frown • \nsubseteq • \nsupseteq • \simeq • \models • \notin • \sqsubset • \sqsupset • \sim • \perp • \mid • \sqsubseteq • \sqsupseteq • \propto • \prec • \succ • \preceq • \succeq • \neq • \sphericalangle • \measuredangle
\(< • > • = • \parallel • \nparallel • \leq • \geq • \doteq • \asymp • \bowtie • \ll • \gg • \equiv • \vdash • \dashv • \subset • \supset • \approx • \in • \ni • \subseteq • \supseteq • \cong • \smile • \frown • \nsubseteq • \nsupseteq • \simeq • \models • \notin • \sqsubset • \sqsupset • \sim • \perp • \mid • \sqsubseteq • \sqsupseteq • \propto • \prec • \succ • \preceq • \succeq • \neq • \sphericalangle • \measuredangle\)
Division Sign and Other Similar Signs
\pm • \cap • \diamond • \oplus • \mp • \cup\text{ }• \bigtriangleup • \ominus • \times • \uplus • \bigtriangledown • \otimes • \div • \sqcap • \triangleleft • \oslash • \ast • \sqcup • \triangleright • \odot • \star • \vee • \bigcirc • \circ • \dagger • \wedge •\text{ }{\color{red}\bullet} • \setminus • \ddagger • \cdot • \wr • \amalg
\(\pm • \cap • \diamond • \oplus • \mp • \cup\text{ }• \bigtriangleup • \ominus • \times • \uplus • \bigtriangledown • \otimes • \div • \sqcap • \triangleleft • \oslash • \ast • \sqcup • \triangleright • \odot • \star • \vee • \bigcirc • \circ • \dagger • \wedge •\text{ }{\color{red}\bullet} • \setminus • \ddagger • \cdot • \wr • \amalg\)
Arrows and Other Similar Symbols
\exists\text{ }• \rightarrow\text{ or }\to •\text{ }\nexists\text{ }• \leftarrow\text{ or }\gets •\text{ }\forall\text{ }• \mapsto •\text{ }\neg\text{ }• \implies • \subset • \Rightarrow \text{ or }\implies • \supset • \leftrightarrow • \in • \iff • \notin • \Leftrightarrow • \ni •\text{ }\top • \land • \bot • \lor • \emptyset • \varnothing
\(\exists\text{ }• \rightarrow\text{ or }\to •\text{ }\nexists\text{ }• \leftarrow\text{ or }\gets •\text{ }\forall\text{ }• \mapsto •\text{ }\neg\text{ }• \implies • \subset • \Rightarrow \text{ or }\implies • \supset • \leftrightarrow • \in • \iff • \notin • \Leftrightarrow • \ni •\text{ }\top • \land • \bot • \lor • \emptyset • \varnothing\)
Barriers and Vertical Arrows
| • \| • / • \backslash • \{ • \} • \langle • \rangle • \uparrow • \Uparrow • \lceil • \rceil • \downarrow • \Downarrow • \lfloor • \rfloor
\(| • \| • / • \backslash • \{ • \} • \langle • \rangle • \uparrow • \Uparrow • \lceil • \rceil • \downarrow • \Downarrow • \lfloor • \rfloor\)
Symbols used for Physics, Calculus, etc
\partial • \imath • \Re • \nabla • \aleph • \eth • \jmath • \Im • \Box • \beth • \hbar • \ell • \wp • \infty • \gimel
\(\partial • \imath • \Re • \nabla • \aleph • \eth • \jmath • \Im • \Box • \beth • \hbar • \ell • \wp • \infty • \gimel\)
Greek
A\alpha • B\beta • \Gamma\gamma • \Delta\delta • E\epsilon\varepsilon • Z\zeta • H\eta • \Theta\theta\vartheta • I\iota • K\kappa • \Lambda\lambda • M\mu • N\nu • \Xi\xi • O\omicron • \Pi\pi\varpi • P\rho\varrho • \Sigma\sigma\varsigma • T\tau • \Upsilon\upsilon • \Phi\phi\varphi • X\chi • \Psi\psi • \Omega\omega
\(A\alpha • B\beta • \Gamma\gamma • \Delta\delta • E\epsilon\varepsilon • Z\zeta • H\eta • \Theta\theta\vartheta • I\iota • K\kappa • \Lambda\lambda • M\mu • N\nu • \Xi\xi • O\omicron • \Pi\pi\varpi • P\rho\varrho • \Sigma\sigma\varsigma • T\tau • \Upsilon\upsilon • \Phi\phi\varphi • X\chi • \Psi\psi • \Omega\omega\)
Cool Stuff to Do
1^{2^{3^{4}}} • 1_{2_{3_{4}}} • ^{\text{lbs}}/_{\text{inches}}\times703=\text{BMI} • \frac{\text{lbs}}{\text{inches}}\times703=\text{BMI}
\(1^{2^{3^{4}}} • 1_{2_{3_{4}}} • \text{ }^{\text{lbs}}/_{\text{inches}}\times703=\text{BMI} • \frac{\text{lbs}}{\text{inches}}\times703=\text{BMI}\)
LATEX Logos
\LaTeX • \TeX
\(\LaTeX • \TeX\)
Boxed Equations
\boxed{y=x+2}
\(\boxed{y=x+2}\)
All fonts:
\textrm{The quick fox jumped over the lazy dog. 0123456789}\\
\textbf{The quick fox jumped over the lazy dog. 0123456789}\\
\textit{The quick fox jumped over the lazy dog. 0123456789}\\
\texttt{The quick fox jumped over the lazy dog. 0123456789}
\(\textrm{The quick fox jumped over the lazy dog. 0123456789}\\ \textbf{The quick fox jumped over the lazy dog. 0123456789}\\ \textit{The quick fox jumped over the lazy dog. 0123456789}\\ \texttt{The quick fox jumped over the lazy dog. 0123456789}\)
How to format to tables:
\begin{array}
\text{Input} & \text{Output} \\
\hline
1 & 4 \\
2 & 8 \\
3 & 12 \\
4 & 16 \\
5 & 20
\end{array}
\(\begin{array}{c|c} \text{Input} & \text{Output} \\ \hline 1 & 4 \\ 2 & 8 \\ 3 & 12 \\ 4 & 16 \\ 5 & 20 \end{array}\)
All colors:
{\color{Apricot}apricot} • {\color{Bittersweet}bittersweet} • {\color{blue}blue} • {\color{blueviolet}blueviolet} • {\color{brown}brown} • {\color{cadetblue}cadetblue} • {\color{Cerulean}cerulean} • {\color{cyan}cyan} • {\color{darkorchid}darkorchid} • {\color{forestgreen}forestgreeen} • {\color{goldenrod}goldenrod} • {\color{green}green} • {\color{JungleGreen}junglegreen} • {\color{limegreen}limegreen} • {\color{Mahogany}mahogany} • {\color{Melon}melon} • {\color{Mulberry}mulberry} • {\color{OliveGreen}olivegreen} • {\color{orangered}orangered} • {\color{Peach}peach} • {\color{PineGreen}pinegreen} • {\color{ProcessBlue}processblue} • {\color{RawSienna}rawsienna} • {\color{RedOrange}redorange} • {\color{Rhodamine}rhodamine} • {\color{RoyalPurple}royalpurple} • {\color{salmon}salmon} • {\color{Sepia}sepia} • {\color{springgreen}springgreen} • {\color{TealBlue}tealblue} • {\color{turquoise}turquoise} • {\color{VioletRed}violetred} • {\color{WildStrawberry}wildstrawberry} • {\color{yellowgreen}yellowgreen}
\({\color{Apricot}apricot} • {\color{Bittersweet}bittersweet} • {\color{blue}blue} • {\color{blueviolet}blueviolet} • {\color{brown}brown} • {\color{cadetblue}cadetblue} • {\color{Cerulean}cerulean} • {\color{cyan}cyan} • {\color{darkorchid}darkorchid} • {\color{forestgreen}forestgreeen} • {\color{goldenrod}goldenrod} • {\color{green}green} • {\color{JungleGreen}junglegreen} • {\color{limegreen}limegreen} • {\color{Mahogany}mahogany} • {\color{Melon}melon} • {\color{Mulberry}mulberry} • {\color{OliveGreen}olivegreen} • {\color{orangered}orangered} • {\color{Peach}peach} • {\color{PineGreen}pinegreen} • {\color{ProcessBlue}processblue} • {\color{RawSienna}rawsienna} • {\color{RedOrange}redorange} • {\color{Rhodamine}rhodamine} • {\color{RoyalPurple}royalpurple} • {\color{salmon}salmon} • {\color{Sepia}sepia} • {\color{springgreen}springgreen} • {\color{TealBlue}tealblue} • {\color{turquoise}turquoise} • {\color{VioletRed}violetred} • {\color{WildStrawberry}wildstrawberry} • {\color{yellowgreen}yellowgreen}\)
{\color{aquamarine}aquamarine} • {\color{bluegreen}bluegreen} • {\color{brickred}brickred} • {\color{burntorange}burntorange} • {\color{carnationpink}carnationpink} • {\color{cornflowerblue}cornflowerblue} • {\color{dandelion}dandelion} • {\color{emerald}emerald} • {\color{fuchsia}fuchsia} • {\color{gray}gray} • {\color{greenyellow}greenyellow} • {\color{lavender}lavender} • {\color{magenta}magenta} • {\color{maroon}maroon} • {\color{midnightblue}midnightblue} • {\color{navyblue}navyblue} • {\color{orange}orange} • {\color{orchid}orchid} • {\color{periwinkle}periwinkle} • {\color{plum}plum} • {\color{purple}purple} • {\color{red}red} • {\color{redviolet}redviolet} • {\color{royalblue}royalblue} • {\color{rubinered}rubinered} • {\color{seagreen}seagreen} • {\color{skyblue}skyblue} • {\color{tan}tan} • {\color{thistle}thistle} • {\color{violet}violet} • {\color{white}white}\text{ }(white) • {\color{yellow}yellow} • {\color{yelloworange}yelloworange}
\({\color{aquamarine}aquamarine} • {\color{BlueGreen}bluegreen} • {\color{BrickRed}brickred} • {\color{BurntOrange}burntorange} • {\color{CarnationPink}carnationpink} • {\color{cornflowerblue}cornflowerblue} • {\color{Dandelion}dandelion} • {\color{Emerald}emerald} • {\color{fuchsia}fuchsia} • {\color{gray}gray} • {\color{greenyellow}greenyellow} • {\color{lavender}lavender} • {\color{magenta}magenta} • {\color{maroon}maroon} • {\color{midnightblue}midnightblue} • {\color{NavyBlue}navyblue} • {\color{orange}orange} • {\color{orchid}orchid} • {\color{Periwinkle}periwinkle} • {\color{plum}plum} • {\color{purple}purple} • {\color{red}red} • {\color{RedViolet}redviolet} • {\color{royalblue}royalblue} • {\color{RubineRed}rubinered} • {\color{seagreen}seagreen} • {\color{skyblue}skyblue} • {\color{tan}tan} • {\color{thistle}thistle} • {\color{violet}violet} • {\color{white}white}\text{ }(white) • {\color{yellow}yellow} • {\color{YellowOrange}yelloworange}\)
More fractions:
Warning: When you type a number and then a symbol and a fraction in this code, this fraction is overspaced, like described above. If you write it like this, that won't change. The first one is the only one that's the fixed fraction.
^3/_7 \to ^3/_7 • ^3\text{/}_7 \to ^3\text{/}_7
\(^3/_7 \to ^3/_7 • ^3\text{/}_7 \to ^3\text{/}_7\)
To fix this, type \text{ } on the left side of each fraction that you type. You must also do it this way when writing equations:
^3/_7 \to\text{ }^3/_7 • \text{ }^3\text{/}_7\\
^3/_7 +\text{ }^1/_7=\text{ }^4/_7
\(^3/_7 • \text{ }^3\text{/}_7 \\ ^3/_7 +\text{ }^1/_7=\text{ }^4/_7\)
Empty Boxes and Spacing
\begin{align}...
2\frac{1}{2}&=\boxed{\phantom{00}}\\...
&=\phantom{0}\frac{5}{2}...
\end{align} • insert~space •.insert\phantom{0}phantom\phantom{0}space • \begin{split}
\int_\boxed{}^\boxed{}\boxed{\phantom{0}}~dx...
\end{split}..
Note: The left figure for fractions is spacing called "phantom". "Phantom" is ideal for making empty boxed equations. The center figures show on the left a space using a tilde, and on the right a "phantom space" using the following command. The figure on the right shows a blank integral; the smaller boxes don't need a "phantom space" as the bigger box needs one.
\(\begin{align} 2\frac{1}{2}&=\boxed{\phantom{00}}\\ &=\phantom{0}\frac{5}{2} \end{align} • insert~space • insert\phantom{0}phantom\phantom{0}space • \begin{split} \int_\boxed{}^\boxed{}\boxed{\phantom{0}}~dx \end{split}\)
Fixed Limits
\lim\limits_{x \to \infty} \exp(-x) = 0
Note: Type "/lim", then "/limits" to fix the underset.
\(\lim\limits_{x \to \infty} \exp(-x) = 0\)
1-Variable Statistics
\begin{array}{c|c}
~ & x & freq \\
\hline
1 & 1 & 1 \\
2 & 2 & 2 \\
3 & 3 & 3 \\
4 & 4 & 4 \\
5 & 5 & 5 \\
6 & 6 & 5 \\
7 & 7 & 4 \\
8 & 8 & 3 \\
9 & 9 & 2.\\
10 & 10 & 1 \\
\end{array} ~~~ \begin{align}
\Sigma x^2 &= 1055 \\
\Sigma x &= 165 \\
n &= 30.\\
\overline{x} &= 5.5 \\
\sigma x &= 2.217355783 \\
\text{S}x &= 2.255262046 \\
\text{min}x &= 1 \\
\text{Q}1 &= 4 \\
\text{med} &= 5.5 \\
\text{Q}3 &= 7 \\
\text{max}x &= 10
\end{align}
\(\begin{array}{c|c} ~ & x & freq \\ \hline 1 & 1 & 1 \\ 2 & 2 & 2 \\ 3 & 3 & 3 \\ 4 & 4 & 4 \\ 5 & 5 & 5 \\ 6 & 6 & 5 \\ 7 & 7 & 4 \\ 8 & 8 & 3 \\ 9 & 9 & 2 \\ 10 & 10 & 1 \\ \end{array} ~~~ \begin{align} \Sigma x^2 &= 1055 \\ \Sigma x &= 165 \\ n &= 30 \\ \overline{x} &= 5.5 \\ \sigma x &= 2.217355783 \\ \text{S}x &= 2.255262046 \\ \text{min}x &= 1 \\ \text{Q}1 &= 4 \\ \text{med} &= 5.5 \\ \text{Q}3 &= 7 \\ \text{max}x &= 10 \end{align}\)
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