Symbols:Arithmetic and Algebra

Addition
$$+$$

"Plus", or "added to". A binary operation on two numbers or variables.

Its LaTeX code is +.

See Set Operations and Relations and Abstract Algebra for alternative definitions of this symbol.

Subtraction
$$-$$

"Minus", or "subtract". A binary operation on two numbers or variables.

Its LaTeX code is -.

See Set Operations and Relations and Logical Operators for alternative definitions of this symbol.

Times
$$\times$$

"Times", or "multiplied by". A binary operation on two numbers.

Usually used when numbers are involved (as opposed to letters) to avoid confusion with the use of "$$\cdot$$" which could be confused with the decimal point.

The symbol $$\times$$ is cumbersome in the context of algebra, and may be confused with the letter $$x$$.

Invented by William Oughtred in his 1631 work Clavis Mathematicae.

Its LaTeX code is \times.

See Set Operations and Relations and Vector Algebra for alternative definitions of this symbol.

Dot
$$\cdot$$

$$x \cdot y$$ means $$x$$ times $$y$$, or $$x$$ multiplied by $$y$$, a binary operation on two numbers.

Its LaTeX code is \cdot.

See Vector Algebra, Abstract Algebra and Logical Operators: Deprecated Symbols for alternative definitions of this symbol.

Division
$$\div$$, $$/$$

"Divided by". A binary operation on two numbers.

$$x \div y$$ and $$x / y$$ mean "$$x$$ divided by $$y$$", or $$x \times y^{-1}$$.

$$x / y$$ can also (and often is - it tends to improve comprehension for complicated expressions) be rendered $$\frac {x} {y}$$.

$$x \div y$$ is rarely seen outside grade school.

Their LaTeX codes are as follows:
 * $$x \div y$$: x \div y
 * $$x / y$$: x / y
 * $$\frac {x} {y}$$: \frac {x} {y}

Plus and Minus
$$\pm$$

"Plus or minus. $$a \pm b$$ means "$$a + b$$ or $$a - b$$", often seen when expressing the two solutions of a quadratic equation.

Its LaTeX code is \pm.

See Numerical Analysis for an alternative definition of this symbol.

Sum
$$\sum$$

"Sum". $$\sum_{i=a}^{n} x_i$$ is the addition of the elements of the sequence $$x_i$$ for $$i$$ from $$a$$ to $$n$$ (inclusive).

Its LaTex code is \sum_{a}^{b}</tt>. This will render $$\sum_{a}^{b}$$.

Product
$$\prod$$

"Product". $$\prod_{i=a}^{n}$$ is the multiplication of the elements of the sequence $$x_i$$ for $$i$$ from $$a$$ to $$n$$ (inclusive).

Its LaTeX code is \prod_{a}^{b}</tt>. This will render $$\prod_{a}^{b}$$.

Absolute Value
$$\left|{x}\right|$$

The absolute value of the variable $$x$$, when $$x \in \R$$.

$$ \left|{x}\right| = \begin{cases} x & : x > 0 \\ 0 & : x = 0 \\ -x & : x < 0 \end{cases} $$

The LaTeX code for this is \left|{x}\right|</tt> or \left \vert{x}\right \vert</tt>.

See Set Operations and Relations, Complex Analysis and Abstract Algebra for alternative definitions of this symbol.

Binomial Coefficent
$$\binom n m$$ is interpreted as $$ \binom n m = \begin{cases} \displaystyle \frac {n!} {m! \left({n - m}\right)!} & : m \le n \\ 0 & : m > n \end{cases} $$.

Its LaTeX code is \binom n m</tt> or n \choose m</tt>.

Negation
$$\not=, \not>, \not<, \not\geq, \not\leq$$

"Negation". The above symbols all mean the opposite of the non struck through version of the symbol.

For example, $$x \not= y$$ means that $$x$$ is not equal to of $$y$$.

The LaTeX code for negation is \not</tt> followed by the code for whatever symbol you want to negate. For example, \not \geq</tt> will render $$\not\geq$$.

Note that several of the above relations also have their own LaTeX commands for their negations, for example \ne</tt> or \neq</tt> for \not =</tt>.