Numeracy, Maths and Statistics - Academic Skills Kit

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Types of Numbers

Types of Numbers

Numbers can be classified into sets of numbers according to their properties. The table below lists the names, properties of and symbols used for the main number types.

Note: Many numbers are included in more than one set.

Name	Symbol	Properties	Set/Examples
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 ( $bi$ ).	$1+2i, 1, i, -3i, 0, -5+i$ .

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