CARDINALITY Meaning and
Definition
-
Cardinality refers to the number of elements in a set. It is a concept that is often used in mathematics, specifically in set theory and combinatorics. The cardinality of a set can be finite or infinite.
In the case of a finite set, the cardinality refers to the count of elements it contains. For example, if a set contains three distinct elements, its cardinality is three.
On the other hand, infinite sets have a different notion of cardinality. The cardinality of an infinite set represents the size of the set in comparison to other infinite sets. Mathematicians use various methods to compare the cardinality of different infinite sets, such as bijection or correspondences between the elements.
Cardinality is denoted using various notations, including the "pipe" symbol (|) or a vertical bar, as well as the lowercase letter "n" inside sets. The cardinality of a set A, for instance, can be denoted as |A| or n(A).
Understanding the cardinality of sets is essential in various mathematical fields, such as combinatorics, probability theory, and calculus. It helps mathematicians analyze the properties of sets, determine the size of a sample space, and assess the probability of events occurring. Furthermore, cardinality aids in comparing the relative sizes of different sets and understanding the structure and properties of infinite sets.
Common Misspellings for CARDINALITY
Etymology of CARDINALITY
The word "cardinality" originated from the Latin word "cardinalis", which means "pertaining to a hinge". This Latin word is derived from the noun "cardo", meaning "hinge" or "axis". In the context of mathematics, "cardinality" refers to the measure of the number of elements in a set or the size of a set. The term was first introduced in mathematics and set theory during the late 19th and early 20th centuries.
Infographic
Add the infographic to your website:
