Real numbers have a number of components. Some of these components are:

• They are all natural numbers

Natural numbers are all the numbers that can be divided by themselves, to achieve the answer 1. Examples of real numbers are 1,2,3,4,5,6,7 etc. Natural numbers are used primarily for counting purposes, although they can also be used for placing items in order.

• Whole numbers

These are numbers that contain no fractions. Zero (0) can be included in the list of whole numbers.

• The set of integers

Integers are all whole numbers, and natural numbers, and also include negative numbers. They must not be written with a fractional element.

• Rational numbers

These numbers are any number that can be expressed as a fraction of two integers. Zero can be classed as a rational number and an integer, as zero divided by itself, is zero.

• Irrational numbers

An irrational number is classed as a real number, despite the fact that the numbers cannot be written, or expressed as a fraction.

Real numbers are formalized using a set theory, known as Zermeki-Fraenkel Axiomatization. The way real numbers work in mathematics is a constant question that is being raised by mathematicians. Some believe that non-standard real numbers are in fact real, whilst some believe that real numbers can only fall into the categories that are listed above.

A real number is the only type of number that is used in the world of science, as most physical elements are measured using real numbers, like mass, speed and position. Computing does not use real numbers, but does use a standard set of rational numbers.

• They are all natural numbers

Natural numbers are all the numbers that can be divided by themselves, to achieve the answer 1. Examples of real numbers are 1,2,3,4,5,6,7 etc. Natural numbers are used primarily for counting purposes, although they can also be used for placing items in order.

• Whole numbers

These are numbers that contain no fractions. Zero (0) can be included in the list of whole numbers.

• The set of integers

Integers are all whole numbers, and natural numbers, and also include negative numbers. They must not be written with a fractional element.

• Rational numbers

These numbers are any number that can be expressed as a fraction of two integers. Zero can be classed as a rational number and an integer, as zero divided by itself, is zero.

• Irrational numbers

An irrational number is classed as a real number, despite the fact that the numbers cannot be written, or expressed as a fraction.

Real numbers are formalized using a set theory, known as Zermeki-Fraenkel Axiomatization. The way real numbers work in mathematics is a constant question that is being raised by mathematicians. Some believe that non-standard real numbers are in fact real, whilst some believe that real numbers can only fall into the categories that are listed above.

A real number is the only type of number that is used in the world of science, as most physical elements are measured using real numbers, like mass, speed and position. Computing does not use real numbers, but does use a standard set of rational numbers.