Symbols:Arithmetic and Algebra
Symbols used in Arithmetic and Algebra
Addition
- $+$
Plus, or added to.
A binary operation on two numbers or variables.
Its $\LaTeX$ code is + .
Positive Quantity
- $+$
A unary operator prepended to a number to indicate that it is positive.
For example:
- $+5$
If a number does not have either $+$ or $-$ prepended, it is assumed to be positive by default.
The $\LaTeX$ code for \(+5\) is +5 .
Subtraction
- $-$
Minus, or subtract.
A binary operation on two numbers or variables.
Its $\LaTeX$ code is - .
Negative Quantity
- $-$
A unary operator prepended to a number to indicate that it is negative.
For example:
- $-6$
The $\LaTeX$ code for \(-6\) is -6 .
Multiplication (Arithmetic)
- $\times$
Times, or multiplied by.
A binary operation on two numbers or variables.
Usually used when numbers are involved (as opposed to variables) 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 $x$.
Its $\LaTeX$ code is \times .
Multiplication (Algebra)
- $\cdot$
$x \cdot y$ means $x$ times $y$, or $x$ multiplied by $y$.
A binary operation on two variables.
Usually used when variables are involved (as opposed to numbers) to avoid confusion with the use of $\times$ which could be confused with the symbol $x$ when used as a variable.
It is preferred that the symbol $\cdot$ is not used in arithmetic between numbers, as it can be confused with the decimal point.
Its $\LaTeX$ code is \cdot .
Division
- $\div$, $/$
A binary operation on two numbers or variables.
$x \div y$ 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:
- The $\LaTeX$ code for \(x \div y\) is
x \div y. - The $\LaTeX$ code for \(x / y\) is
x / y. - The $\LaTeX$ code for \(\dfrac {x} {y}\) is
\dfrac {x} {y}.
Plus or Minus
- $\pm$
$a \pm b$ means $a + b$ or $a - b$, often seen when expressing the two solutions of a quadratic equation.
Its $\LaTeX$ code is \pm .
Absolute Value
- $\size x$
The absolute value of the variable $x$, when $x \in \R$.
$\size x = \begin {cases} x & : x > 0 \\ 0 & : x = 0 \\ -x & : x < 0 \end {cases}$
The $\LaTeX$ code for \(\size x\) is \size x .
Binomial Coefficient
- $\dbinom n m$
The binomial coefficient, which specifies the number of ways you can choose $m$ objects from $n$ (all objects being distinct).
Formally defined as:
- $\dbinom n m = \begin {cases} \dfrac {n!} {m! \, \paren {n - m}!} & : m \le n \\ 0 & : m > n \end {cases}$
The $\LaTeX$ code for \(\dbinom {n} {m}\) is \dbinom {n} {m} or \displaystyle {n} \choose {m}.