Number Systems (Leaving Cert Mathematics): Flashcards

$N = \{1, 2, 3, 4, 5, ...\}$ - positive counting numbers

No, natural numbers do not include zero or negatives

$Z = \{..., -3, -2, -1, 0, 1, 2, 3, ...\}$

Zero and negative numbers

Numbers written as $\frac{a}{b}$ where $a, b \in Z$ and $b \neq 0$

Terminating decimals and recurring decimals

Numbers that cannot be expressed as fractions

Non-terminating, non-repeating decimals

$\sqrt{2}$, $\sqrt{3}$, $\sqrt{5}$, $\pi$

All rational and irrational numbers combined

$N \subset Z \subset Q \subset R$

'Is an element of' or 'belongs to'

Any integer $n$ can be written as $\frac{n}{1}$

No, e.g. $\sqrt{4} = 2$ and $\sqrt{16} = 4$ are rational

Irrational number ($\frac{22}{7}$ is just an approximation)