What is the set?

January 25, 2015
What is the set?

A set is a collection of certain objects united according to a certain rule. At the same time, they retain their individual traits. We meet sets in everyday life: a set of coins in a wallet, plates in a closet, apples in a refrigerator, etc. It is also a mathematical concept that is axiomatic.

Mathematical set

The fact that such a set, we know thanks to George Kantor, who devoted his mathematical works to this topic. Set theory has become a real revolution in this field of science and to this day is of great importance for the study of more complex concepts. A set can be defined only by specifying all the objects included in it and depicted as follows:

  • M = {a, b, c ...}

The item belonging to the set is indicated by the sign "« ". All elements of the set must be different from each other. If no elements are included in the set, it is usually called empty.

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

Operations performed on sets

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

  • An association. The sum of the given sets is denoted as X = N + M + P. The union must contain the totality of all the elements of at least one of the components.
  • Intersection The common part of several sets is called an intersection and is denoted as Y. If the intersection of the sets is empty, they are considered to not intersect.
  • Difference. A difference is a collection of elements of one set that do not belong to another.

Set of numbers

The set consisting of numbers is called numeric.

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

  • 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 that we use when counting. They arise naturally);
  • R - consisting of real numbers (positive, negative numbers and zero are called real. They are rational and irrational.Irrational numbers can only be expressed in decimal format (9.999999999).

Having understood what a set of numbers is, it will be easier for you to further comprehend mathematics. This interesting science develops logical thinking, requires patience, filigree accuracy and time, but gives great joy from solving complex problems.

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