In Real Analysis you study real numbers and their properties.

The classification of real numbers (using set notation) goes like this:

**natural numbers**are the set of numbers we use for counting, $\mathbb{N}$**whole numbers**are the set of numbers we count with plus the number zero, $\mathbb{Z^+}$**integers**are the set of natural numbers, their opposites, and zero, $\mathbb{Z}$**rational numbers**are the set of numbers that are ratios of integers, $\mathbb{Q}$- as a caveat, the denominator should be $\neq 0$
- they can be represented as decimal numbers as well (terminating or repeating)

**irrational numbers**are the set of numbers that can’t be represented as a fraction, $\mathbb{I}$

There are also a few others but they belong to more advanced treatments of number theory. Because of these definitions, some numbers may belong to multiple groups. Below is a diagram of these categories.

*Fig 1. Classifying real numbers*

These numbers have a bunch of properties that are useful shortcuts when doing calculations by hand.