Numeracy, Maths and Statistics - Academic Skills Kit (2024)

Integers

$\mathbb{Z}$

All positive and negative whole numbers.

$\{...-1, -2 , 0, 1, 2, ...\}$

Natural

$\mathbb{N}$

Numbers used for counting (all positive integers).

$0, 1, 2, ...$

Real

$\mathbb{R}$

Includes all numbers on the number line.

$\frac{1}{5}, \sqrt{\frac{1}{5}}, 0, -2$

Rational

$\mathbb{Q}$

All real numbers which can be expressed as a fraction, $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. All integers are rational numbers as 1 is a non-zero integer.

$\frac{1}{5}, \frac{5}{1} (=5), \frac{2}{3}, \frac{3}{2}, \frac{0}{3} (=0)$

Irrational

$\mathbb{I}$

All real numbers which can't be expressed as a fraction whose numerator and denominator are integers (i.e. all real numbers which aren't rational).

$\pi, \sqrt{2}, \sqrt{3}$

Imaginary

NA

Numbers which are the product of a real number and the imaginary unit $i$ (where $i=\sqrt{-1}$).

$3i=\sqrt{-9}, -5i=-\sqrt{-25}, 3\sqrt{2}i=\sqrt{-18}$

Complex

$\mathbb{C}$

All numbers which can be expressed in the form $a+bi$ where $a$ and $b$ are real numbers and $i=\sqrt{-1}$. Each complex number is a combination of a real number ($a$) and an imaginary number ($bi$).

$1+2i, 1, i, -3i, 0, -5+i$.