MYP Standard Mathematics The Number System Key Definitions

The set of elements not in a set. The complement of $A$ (relative to $U$) is $A'$.

The integers $\mathbb{Z}$ are the whole numbers and their negatives: $\{\dots,-3,-2,-1,0,1,2,3,\dots\}$.

An irrational number is a real number that cannot be written in the form $\frac{a}{b}$ with integers $a$ and $b\neq 0$. The set of irrationals is often written $\mathbb{Q}'$.

The natural numbers $\mathbb{N}$ are the counting numbers. Depending on convention, $0$ may or may not be included.

A rational number $q$ is any number that can be written as a fraction $q=\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b\neq 0$.

The real numbers $\mathbb{R}$ are all numbers that can be placed on the number line, including both rational and irrational numbers.

A collection of objects. Each object in the set is called an element (or member) of the set.

A set $A$ is a subset of $B$ (written $A\subseteq B$) if every element of $A$ is also an element of $B$.