Number Systems

\(\mathbb N\): The set of natural or counting numbers 0, 1, 2, 3, etc. Some say this set does not include zero.

\(\mathbb Z\): The set of integers. This set is the same as the set of natural numbers but includes the negative whole numbers.

\(\mathbb Q\): The set of rational numbers. These are the numbers that can be expressed as a proper fraction or one integer divided by another.

\(\mathbb R\): The set of real numbers. That is probably all the numbers you know unless you have studied the topic of Complex Numbers.

$$\mathbb R$$
$$\mathbb Q$$
$$\mathbb Z$$
$$\mathbb N$$
\(\text{one million}\)
\(\cos 40^o\)
\(\sin 30^o\)
Featured Activity

Code Cracker

Code Cracker

Learn the basic techniques for cracking codes then practise them using this interactive challenge. There are three levels of difficulty and many different messages to decipher.


Drag the numbers into the correct sets as shown in the Venn diagram above. When you have finished click on the 'Check' button above.

There is a solution and ad-free version of this activity available to those who have a Transum Subscription.

There are other related activities on the Transum Mathematics website to support your understanding of number.

Venn Diagram Sieve of Eratosthenes Satisfaction Recurring Decimals Number
Recently Updated

Yes No Questions

Yes No Questions

A game to determine the mathematical item by asking questions that can only be answered yes or no. So far this activity has been accessed 22 times and it is ready for you to enjoy!

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


©1997-2017 WWW.TRANSUM.ORG