Number Sets
Table of Contents

We will look at some common number sets that will arise frequently in the modern algebra section:

Symbol for Number Set Name of Number Set Examples
$\mathbb{R}$ Real Numbers -1922.33 -2, 0, 1.331, $\pi$, 3/2, …
$\mathbb{Q}$ Rational Numbers All real numbers q that can be written in the form $q = \frac{a}{b}$ where b ≠ 0. For example, 2/5, 9/2, 3/1, 27/6, …
$\bar{\mathbb{Q}}$ or $\mathbb{R} - \mathbb{Q}$ Irrational Numbers All real numbers q that cannot be written in the form $q = \frac{a}{b}$. For example, $\pi, \tau, e$, … (Note that notation for irrational numbers is not standard).
$\mathbb{N}$ Natural Numbers All whole numbers starting from 1 upwards, for example 1, 2, 3, … (Note that sometimes the natural numbers are defined to include 0, while other times they are not).
$\mathbb{Z}$ Integers All positive and negative whole numbers including zero, for example …, -2, -1, 0, 1, 2, …
$\mathbb{Z}^+$ Positive Integers All positive whole numbers, for example 1, 2, 3, …
$\mathbb{I}$ Imaginary Numbers Any number in the form $\sqrt{a}$ where a is negative, for example $\sqrt{-3}$
$\mathbb{C}$ Complex Numbers Any number in the form $z = a + bi$ where "a" is considered the real part and "bi" is considered the imaginary part ($i = \sqrt{-1}$). For example, 3 + 2i, -4 + 0i, 0 + 2i, etc…
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