# 1.1: Background regarding numbers

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The natural numbers (denoted by $$\mathbb{N}$$ are the numbers

$1,2,3,4,5, \dots \nonumber$

The integers (denoted by $$\mathbb{Z}$$ are the numbers

$\dots,-4,-3,-2,-1,0,1,2,3,4,5, \dots \nonumber$

The rational numbers (denoted by $$\mathbb{Q}$$ are the fractions $$\frac{a}{b}$$ of integers $$a$$ and $$b$$ with $$b\neq 0$$. Here are some examples of rational numbers:

$\frac{3}{5}, -\frac{2}{6}, 17, 0, \frac{3}{-8} \nonumber$

The real numbers (denoted by $$\mathbb{R}$$ are the numbers on the real number line Here are some examples of real numbers:

$\sqrt{3}, \pi, -\frac{2}{5}, 18, 0, 6.789 \nonumber$

A real number that is not a rational number is called an irrational number. Here are some examples of irrational numbers:

$\pi, \sqrt{2}, 5^{\frac{2}{3}}, e \nonumber$

This page titled 1.1: Background regarding numbers is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Thomas Tradler and Holly Carley (New York City College of Technology at CUNY Academic Works) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.