cardinality of a set
The cardinality of a set is a term used in mathematics to describe the “size” or “number of elements” in a set
The cardinality of a set is a term used in mathematics to describe the “size” or “number of elements” in a set. It measures the amount of distinct elements present in a set, regardless of their order or repetition.
The cardinality of a set A is denoted as |A| or “the absolute value of A.” It is a non-negative integer that represents the number of elements in the set. For example, if we have a set A = {2, 4, 6, 8}, then the cardinality of A, denoted as |A|, is 4 since there are four distinct elements in the set.
Another example would be a set B = {1, 3, 1, 5, 3}. In this case, even though the number 1 and 3 are repeated, the cardinality of B is still 3 because there are three distinct elements in the set.
Sets can have different cardinalities. For example, the empty set (∅), which has no elements, has a cardinality of 0. Conversely, the set of all natural numbers (N) has an infinite cardinality, denoted as |N| = ∞, since it contains an unlimited number of elements.
Cardinality is an important concept in set theory and has various applications in different branches of mathematics, such as counting and combinatorics. It allows us to compare the sizes of different sets and study their properties.
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