# How do you classify real numbers?

##### 2 Answers

Irrational and rational numbers

Rational numbers: integers, whole numbers, counting/natural numbers

#### Explanation:

Real numbers are either irrational or rational. Rational numbers can be written as fractions (using two integers, such as

Rational numbers:

Irrational numbers:

There are several different groups of rational numbers. There are integers, whole numbers, and counting/natural numbers. Integers do not have decimals. They can be positive or negative.

Integers:

Whole numbers are all non-negative integers. Examples include

Natural/counting numbers are all positive integers. (We don't start counting from zero).

Counting numbers:

Read below.

#### Explanation:

Let's start with counting numbers.

These are whole numbers you are familiar with.

Any opposite numbers to counting numbers are negative whole numbers.

All of these numbers and

Now, any number that can be written as a fraction

Any number that can't be written as

All of the rational numbers and irrational numbers are considered real numbers. Notice here that all of these numbers lie on a straight number line.

Any number that lies outside the number line is a not real number.

For example, we can extend the 1-D line to 2-D plane with complex numbers on it.

You could even extend the plane to 4-D space and even to 8-D space. Interestingly, that is where the extension stops. Note here that there is no 3-D number system nor any number between 3 and 8.