universal set
Quick Summary
In mathematics, a universal set is a collection of all elements relevant to a specific discussion or problem, also known as the universe of discourse. This concept is fundamental in set theory, where sets are collections of objects. For example, if you are discussing even and odd numbers, the universal set might be all integers.12
The idea of a universal set helps define operations like the complement of a set. The complement of a set A within a universal set U includes all elements in U that are not in A. While the concept of infinity is related to endless sequences of numbers, the universal set itself is defined within the context of a particular problem.231
Ask Britannica AI about this topic
Britannica doesn't have a full article on this topic, so we've curated a list of our relevant coverage.
formal logicSet theory⌠¡ z â y}; the universal class, symbolized as V, is the class of which everything is a member, definable as the complement of the null classâi.e., as -Î. Î itself is sometimes taken as a primitive individual constant, sometimes defined as {x : x â x}âthe class of objectsâŚ
Read More⌠¡ z â y}; the universal class, symbolized as V, is the class of which everything is a member, definable as the complement of the null classâi.e., as -Î. Î itself is sometimes taken as a primitive individual constant, sometimes defined as {x : x â x}âthe class of objectsâŚ
Read More- set theoryOperations on sets
âŚU, U is called the universal set (or universe). Then for any subset A of U, the complement of A (symbolized by AⲠor U â A) is defined as the set of all elements in the universe U that are not in A. For example, if the universe consistsâŚ
Read MoreâŚU, U is called the universal set (or universe). Then for any subset A of U, the complement of A (symbolized by AⲠor U â A) is defined as the set of all elements in the universe U that are not in A. For example, if the universe consistsâŚ
Read More