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Set theory is the mathematical theory of well-determined collections, called sets, of objects that are called members, or elements, of the set. ... In set theory, however, as is usual in mathematics, sets are given axiomatically, so their existence and basic properties are postulated by the appropriate formal axioms.
Set theory is the mathematical theory of well-determined collections, called sets, of objects that are called members, or elements, of the set. ... So, the essence of set theory is the study of infinite sets, and therefore it can be defined as the mathematical theory of the actual as opposed to potential infinite.
Set theory is the mathematical theory of well-determined collections, called sets, of objects that are called members, or elements, of the set. ... The axioms of set theory imply the existence of a set-theoretic universe so rich that all mathematical objects can be construed as sets.
Set theory is used throughout mathematics. It is used as a foundation for many subfields of mathematics. In the areas pertaining to statistics, it is particularly used in probability. Much of the concepts in probability are derived from the consequences of set theory.
A set in mathematics is a collection of well-defined and distinct objects, considered as an object in its own right. ... The most basic properties are that a set “has” elements, and that two sets are equal (one and the same) if and only if every element of one is an element of the other.
A set is a group or collection of objects or numbers, considered as an entity unto itself. ... Examples include the set of all computers in the world, the set of all apples on a tree, and the set of all irrational numbers between 0 and 1.
In naive set theory, a set is a collection of objects (called members or elements) that is regarded as being a single object. ... For example, the set given by the rule prime numbers less than 10 can also be given by {2, 3, 5, 7}.
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.
A set is well-defined if there is no ambiguity whether an object belongs to it, i.e., a set is defined so that we can always tell what is and what is not a member of the set. Example: C = {red, blue, yellow, green, purple} is well-defined since it is clear what is in the set.
A universal set is the collection of all objects in a particular context or theory. All other sets in that framework constitute subsets of the universal set, which is denoted as an uppercase italic letter U. The objects themselves are known as elements or members of U.
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