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To classify numbers precisely, we use set notation.
Set
A collection of objects. Each object in the set is called an element (or member) of the set.
Subset
A set $A$ is a subset of $B$ (written $A\subseteq B$) if every element of $A$ is also an element of $B$.
Complement
The set of elements not in a set. The complement of $A$ (relative to $U$) is $A'$.
When our "universal set" is the set of real numbers $\mathbb{R}$, the complement $\mathbb{Q}'$ means "all real numbers that are not rational".
The number system is often shown as nested sets: each set sits inside a larger set.
Natural numbers (N)
The natural numbers $\mathbb{N}$ are the counting numbers. Depending on convention, $0$ may or may not be included.
Integers (Z)
The integers $\mathbb{Z}$ are the whole numbers and their negatives: $\{\dots,-3,-2,-1,0,1,2,3,\dots\}$.
Real numbers (R)
The real numbers $\mathbb{R}$ are all numbers that can be placed on the number line, including both rational and irrational numbers.
The most important "containment facts" are:
A key idea in MYP is that rational numbers are precisely the numbers that can be expressed as a fraction.
Rational numbers (Q)
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 $b\neq 0$.
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Paywall
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