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).

1,2,3,4,5,6...

• 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).

0,1,2,3,4,5,6...

• 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.

0,1,2,3,4,5,6...

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

...-3, -2, -1, 0, 1, 2, 3, 4...

• 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.

\frac{2}{3}, 23, -493, 0.583333, \frac{5}{25}...

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

\pi , \sqrt{7}, -\sqrt{2}, e

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:

0.25, -358, 27, 0, \pi , \sqrt{5}, -\sqrt{25}