Conjunt

Conjunt is the Catalan term for "set" in mathematics and logic, referring to a well-defined collection of distinct objects called elements. A set is determined by its members, and whether an object belongs to the set is called membership, written as x ∈ A for an element x in a set A. Sets are typically denoted by capital letters such as A, B, or C.

Notation and examples: A finite set can be written explicitly, for example A = {1, 2, 3}. The set of natural numbers is N = {0, 1, 2, ...}. The empty set, containing no elements, is ∅. Sets are unordered, so {1, 2} = {2, 1}, and they do not contain repeated elements.

Operations: For sets A and B, the union A ∪ B contains elements in A or B or both; the intersection A ∩ B contains elements common to both; the difference A \ B contains elements in A but not in B. The complement of A relative to a universal set U is U \ A.

Relationships: A set A is a subset of B, written A ⊆ B, if every element of A is also in B. Sets can be finite or infinite; the cardinality |A| counts its elements.

Theory and applications: Conjunts are foundational in mathematics and underpin areas such as logic, probability, and computer science. They appear in Venn diagrams, the construction of power sets, and broader developments in set theory, including operations like Cartesian products and mappings between sets. The term is especially common in Catalan mathematical writing and education.