What are natural, whole and rational sets?

First we must know what a set is. When we put together some elements having similar features we can consider it a set. So, we can have a set of colour pencils, a set of fruit or a set of numbers. It is important to say that in order to be considered a set we need to say that if a certain element belongs to the set or not. For instance, in a set of fruit it is easy to say that the strawberry belongs to the set while bread does not. But if we think about another set composed of intelligent people for instance, it cannot be considered a set at all because the notion of what an intelligent person is differs from person to person. Considering the set of numbers, there are five which are considered to be essential to Maths. Each one of these sets has a symbol and the numbers of its elements is infinite.

What is the set of natural numbers?

The set of natural numbers is represented by the symbol `NN` and it contains the following elements: `NN = {1; 2; 3; 4; 5; 6; ...}`. So, it contains all the natural positive numbers. In order to represent the set of natural numbers including zero, you must use the symbol `NN_0`.

What is the set of integers numbers?

The set of integers numbers is represented by the symbol `ZZ` and it includes the following elements: `ZZ = {-2; -1; 0; 1; 2; 3; ...}`. At a certain time in History it was necessary to represent the notion of loss or debt and so the negative numbers appeared and they were joined to the natural numbers to form the integers numbers.

What is the set of rational numbers?

The set of the rational numbers is represented by the symbol `QQ` and it includes the following elements: `QQ = {-2,5; -1; 0; 3,(3); 4,521; ...}`. So, it contains all the integers numbers plus the finite tenths and the periodic infinite ones (numbers with decimal elements, whose decimal part is infinite but it is repeated such as `10//3`).

What is the set of real numbers?

The set of real numbers is represented by the symbol `RR` and it contains the following elements: `RR = {sqrt(3); pi ; 12; 14,3; ...}`. It includes all the numbers belonging to the previous sets plus the non-periodic infinite tenths such as the case of the well known `pi`.

Are there more sets of numbers?

Yes, there are, such as the set of complex numbers represented by the symbol `CC`. There are also others but they are useful for those students who want to get a Maths degree!

Check out our List of Questions to get to know a little more about the most diverse topics related to mathematics. If you have any pertinent (math) question whose answer can not easily be found, send us an email on the Contact page with the question. We will be happy to respond. In the event that you detect any errors in our answers, do not hesitate to contact us!