Subject: Trigonometry

# Real Numbers

## What are Real Numbers?

To understand real numbers, you first need to understand the following categories of numbers:

**Natural Numbers (positive integers)**are all positive whole numbers above zero on a number line. This definition is is generally used in Number Theory and basic mathematics (i.e. Trig).

**Natural Numbers (non-negative integers)**are all non-negative whole numbers on a number line. Note that this would include zero. The definition is generally used in set theory and computer science (more advanced mathematical concepts).

**Whole Numbers**are all positive whole numbers including zero on a number line. Whole numbers are also sometimes interchanged with "integers"; see below for additional information.

**Integers**are all positive, zero and negative whole numbers on a number line:

**Rational Numbers**are made of Natural, Whole and Integer Numbers, however they're described or interchanged. These can also be explained as numbers that could be represented as fractions.

**Irrational Numbers**are numbers that will never repeat, will never terminate and are not the quotient (result of a division) of two integers.

Finally, we can use these definitions to define real numbers:

**Real Numbers**are defined by the whole set of rational and irrational numbers.

Real numbers represent any number you would find on a number line. Real numbers are often denoted with a large **R** in mathematical notations and equations. This **R** represents the set of all real numbers.

## Let's try an Example

Given the following set of real numbers, define which belong to a) natural numbers, b) whole numbers, C) integers, d) rational numbers and e) irrational numbers:

The answers are as follows:

a) 27

b) 27, 0

c) -358, 27, 0, -\sqrt{25}

d) 0.25, -358, 27, 0, -\sqrt{25}

e) \pi, \sqrt{5}