Types of Numbers

Primary tabs

Lesson Summary: 
We describe natural numbers, integers, rational numbers and real numbers.
Lesson Outputs: 
Sets and Set Notation

SAMPLE LESSON

Sign in for easy to read lessons narrowly focused on a specific subject. All lessons are linked to each other allowing you to easily see the connections between different Calculus concepts. Our unique Calcmap will give you a bird's-eye view of all our lessons and help you see how important concepts are related to each other. All of the formulas are available to our subscribers, but here is a sample of the lesson you will see when you log in:



Lesson: 

There are typically five different types of numbers we work with in Calculus:

Number Description
Natural Numbers <Sign in to see all the formulas>. (Note that there is no agreement on whether to include $0$ as a natural number so you may see some people define it as <Sign in to see all the formulas>.)
Integers <Sign in to see all the formulas>
Rational Numbers Numbers that can be expressed as the quotient of two integers ($n/m$ where $n$ and <Sign in to see all the formulas> are integers).
For example, $2/7$, $-9/7$, $7/1=7$.
Irrational Numbers Numbers that are not rational. For example, <Sign in to see all the formulas> and $\pi$ cannot be expressed as the quotient of two integers.
Real Numbers The union of the set of integers, rational numbers, and irrational numbers.

Notice that the set of natural numbers is a subset of the integers. The integers are a subset of the rational numbers. Natural numbers, integers, rational numbers, and irrational numbers are all subsets of the set of real numbers.

Most proofs in Calculus assume that a number is a real number unless explicitly stated as something else.