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.

Multiplication

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

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

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

Their $\LaTeX$ codes are as follows:

• $x \div y$: x \div y
• $x / y$: x / y
• $\dfrac {x} {y}$: \dfrac {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

$\displaystyle \sum$

Sum notation.

$\displaystyle \sum_{k=a}^{n} x_k$ is the addition of the elements of the sequence $x_k$ for $k$ from $a$ to $n$ (inclusive).

Its $\LaTeX$ code is \displaystyle \sum_{a}^{b}. This will render $\displaystyle \sum_{a}^{b}$.

Product

$\displaystyle \prod$

Product notation.

$\displaystyle \prod_{k=a}^{n} x_k$ is the multiplication of the elements of the sequence $x_k$ for $k$ from $a$ to $n$ (inclusive).

Its $\LaTeX$ code is \displaystyle \prod_{a}^{b}. This will render $\displaystyle \prod_{a}^{b}$.

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| or \left \vert{x}\right \vert.

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

Binomial Coefficent

$\displaystyle \binom n m$

The binomial coefficient, which specifies the number of ways you can choose $m$ objects from $n$ (all objects being distinct).

Interpreted as:

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

Its $\LaTeX$ code is \displaystyle \binom n m or \displaystyle n \choose m.

Negation

$\not =, \not >, \not <, \not \ge, \not \le$

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 followed by the code for whatever symbol you want to negate. For example, \not \ge will render $\not \ge$.

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