részhalmazon

Részhalmazon, also known as subset, is a fundamental concept in set theory, a branch of mathematical logic. It refers to a set that is completely contained within another set. In other words, if every element of a set A is also an element of set B, then A is a subset of B, denoted as A ⊆ B. This relationship is known as inclusion.

There are two types of subsets: proper and improper. A proper subset is a subset that is not equal to the original set; it is denoted as A ⊊ B. An improper subset is the set itself, meaning A ⊆ A for any set A.

Subsets are widely used in various areas of mathematics and computer science. They are essential in defining the power set of a set, which is the set of all subsets of a given set. Subsets also play a crucial role in defining relations and functions, as well as in understanding the structure of mathematical objects.

In summary, a subset is a set that is contained within another set. It is a fundamental concept in set theory with wide-ranging applications in mathematics and computer science.