delmængderbegrebet

Delmængdebegrebet is a fundamental concept in set theory, describing the relationship between two sets where one is contained within the other. A set A is considered a delmængde of a set B, denoted as A ⊆ B, if every element that belongs to set A also belongs to set B. This means that A does not contain any elements that are not present in B.

For example, if set A consists of the numbers {1, 2} and set B consists of the numbers {1, 2, 3}, then A is a delmængde of B because both 1 and 2 are elements of B. The empty set, denoted by ∅, is considered a delmængde of every set, including itself. A set is always a delmængde of itself.

The concept of delmængder allows mathematicians to classify and organize elements into groups. It is crucial for understanding more complex mathematical structures and operations, such as set union, intersection, and power sets. The opposite of a delmængde is a overmængde, where B would be an overmængde of A if A ⊆ B.