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Right click over any symbol to see the command used to create it.
$\sim$, $\wedge$, $\vee$, $\cup$, $\cap$, $\bigcup$, $\bigcap$, $\forall$, $\exists$, $\Rightarrow$, $\in$, $\notin$, $\subseteq$, $\not\subseteq$, $\mathcal{P}$, $\mathcal{A}$, $\mathcal{B}$, $\mathcal{C}$, $\mathbb{R}$, $\mathbb{N}$, $\mathbb{Z}$, $\mathbb{W}$, $\square$, $\blacksquare$.
If you want an equation centered with the equal signs aligned, use the align environment. Double click to see the code. Use & to align, and \\ to start a new line. Remember, right click the code below to see the commands used to make it. Then you can copy/paste the code to use it in your own work.
We now compute $$ \begin{align} \underbrace{1+2+3+\cdots + n} + (n+1) &=\frac{n(n+1)}{2}+(n+1) && \text{ (replace using the assumption) }\\ &=(n+1)\left[\frac{n}{2}+1\right] &&\text{ (factor) }\\ &=(n+1)\frac{n+2}{2} &&\text{(get a common denominator).} \end{align} $$
Why $\LaTeX$?
To enter mathematics on the web, we will use the language of $\LaTeX$. $\LaTeX$ is a powerful language which typesets mathematics. Some publishers require that you submit work in $\LaTeX$. The exams, quizzes, and other materials that I provide throughout the semester are created using $\LaTeX$.
This page is designed as a place to quickly find the commands you need to get a certain symbol to appear on the web. You can find additional commands at https://www.artofproblemsolving.com/wiki/index.php/LaTeX:Symbols. Note that not every $\LaTeX$ command will display properly on this website (displaying mathematics on the web is currently under development across the nation). If you are trying to get a certain symbol to work, please email me and I may be able to get it to work.
Another way to find a symbol that is not on this page is to use a web search engine. For example, if you want to find out how to create a large sigma for using in sigma notation, search for "Latex sigma sum". Most of the time you will find a page that quickly shows you the command you use to produce a sigma.
Currently I use a program called MathJax to display mathematics on the web. One nice feature of MathJax is that you can double click on a math symbol and it will show you the syntax used to create that symbol.
Syntax Examples
We enclose all math symbols inside of single dollar signs \$ \$ or double dollar signs \$\$ \$\$. This tells the computer that we have entered math mode. One easy way to place \$ \$ around some text is to highlight the text and then select the sqrt{n} button from the editor. Double dollar signs center the mathematics on its own line.
Here is a long list of some examples. Right click over any example that you want to see the code for.
$A$, $A=B$, $|P_1 P_2|$, $\frac{x}{y}$, $A_1$, $A_{n+1}$, $x_{1}^{3}$, $x_{n+1}^{m-2}$, $x<y$, $x\leq y$, $x\geq y$, $x\neq y$, $\{x|P(x)\}$, $\emptyset$, $\sum$, $\sum_{n=1}^{\infty}$, $\displaystyle\sum_{n=1}^{\infty}$, $$\sum_{n=1}^{\infty}$$, ${\mathbb{R}}$, ${\mathbb{Z}}$, $\alpha$, $\beta$, $\gamma$, $\lambda$, $\Lambda$, $\delta$, $\Delta$, $f\circ g: A\to B$, $\hat{x}$, $\bar{x}$, $A\times B$, $A\cdot B$, $x_1+x_2+\cdots+x_{n-1}+x_n$, $A\approx B$, $\sin x \cos x \tan x \cot x \sec x \csc x$, $(\frac{1}{n})$, $\left(\frac{1}{n}\right)$, $$|x|= \begin{cases} x \text{ if } x\geq 0\\ -x \text{ if } x<0 \end{cases}, $$ $ \left<1,2,4 \right> $, $1\vec{i} + 1\vec{j} +1 \vec{k} $ , $f^\prime$, $ \int f(x) dx $, $ \int_a^b f(x) dx $, $ \displaystyle\int_a^b f(x) dx = F(x)\bigg|_a^b $, $$ \int_a^b f(x) dx, $$ $ \frac{d}{dx}[f(x)] $, $$ \frac{d}{dx}[f(x)]. $$
Lining up calculations accross multiple lines.
The following examples show you how to line up an equation.
- Find the derivative of $f(x)=x^2$ using the definition of the derivative.
We use the definition of the derivative by computing $$ \begin{align} \lim_{h\to 0} \frac{f(x+h)-f(x)}{h} &= \lim_{h\to 0} \frac{(x+h)^2-x^2}{h}\\ &= \lim_{h\to 0} \frac{x^2+2xh+h^2-x^2}{h}\\ &= \lim_{h\to 0} \frac{2xh+h^2}{h}\\ &= \lim_{h\to 0} 2x+h\\ &= 2x. \end{align} $$ This shows that the derivative is $f^\prime(x) = 2x$.
The & symbols line up the equation, and \\ means create a new line. You have to start the align environment, and end it. Feel free to copy the syntax and take it to your homepage (Profiles) and play with the options there. Please don't edit this page.