# What is a set?

A set is a set of certainunited by a certain rule of objects. In doing so, they retain their individual characteristics. We meet sets in everyday life: a collection of coins in a purse, plates in a closet, apples in a refrigerator, etc. It is also a mathematical concept, which is axiomatic.

## Mathematical set

We know about such a multitude thanks toGeorg Cantor, who devoted his mathematical works to this topic. Set theory has become a veritable revolution in this field of science and to this day is of great importance for the study of more complex concepts. The set can be defined only by asking all the objects included in it, and represented as follows:

- M = {a, b, c ...}

The affiliation of an object to a set is denoted by the sign "Є". All elements of the set must be different from each other. If no element enters the set, it is usually called empty.

Elements of one set can be part of another. Sets consisting of identical elements are considered to be equal.

## The operations performed on sets

Having analyzed what is called a set, one can proceed to a description of the actions on them.

- An association. The sum of given sets is denoted by X = N + M + P. The union must contain the totality of all elements of at least one of the summands.
- Intersection. The common part of several sets is called the intersection and is denoted by Y. For an empty intersection of sets it is assumed that they do not intersect.
- Difference. A difference is a collection of elements of one set not belonging to another.

## The set of numbers

A set consisting of numbers is called numeric.

In accordance with the types of incoming elements of the set can be designated:

- Z - consisting of integers (the range of infinity of positive and negative numbers);
- Q - consisting of rational numbers (ie represented by a fraction);
- N - consisting of natural numbers (natural numbers are those we use when counting, they arise naturally);
- R - consisting of real numbers(positive, negative, and zero are called real, they are rational and irrational.) Irrational numbers can only be expressed in decimal form (9.999999999).

Having analyzed what a set of numbers is, it's easier for youwill further comprehend mathematics. This interesting science develops logical thinking, requires patience, filigree precision and time, but gives great joy from solving complex problems.

Lovers of mathematics will also be interested in the article How many numbers exist.