In the field of mathematics, two sets A and B are equinumerous if they have the same cardinality, i. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and In Mathematics, the cardinality of a set is a measure of the "number of elements of the set" e. , if there exists a bijection f : A → B. In Mathematics, a bijection, or a bijective function is a function f from a set X to a set Y with the property This is usually denoted
or 
.
The study of cardinality is often called equinumerosity (equalness-of-number). The terms equipollence (equalness-of-strength) and equipotence (equalness-of-power) are sometimes used instead.
In Set, the category of all sets with functions as morphisms, an isomorphism between two sets is precisely a bijection, and two sets are equinumerous precisely if they are isomorphic in this category. In Mathematics, the category of sets, denoted as Set, is the category whose objects are all sets and whose Morphisms are In Mathematics, a category is a fundamental and abstract way to describe mathematical entities and their relationships The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function In Abstract algebra, an isomorphism ( Greek: ἴσος isos "equal" and μορφή morphe "shape" is a bijective
See also
In Mathematics, the category of sets, denoted as Set, is the category whose objects are all sets and whose Morphisms are This article describes cardinal numbers in mathematics For cardinals in linguistics see Names of numbers in English. In Mathematics, the cardinality of a set is a measure of the "number of elements of the set" In Mathematics, a bijection, or a bijective function is a function f from a set X to a set Y with the propertyDapyx Software network: MP3 Explorer | Ebook Manager | Zenithic