Intersectia

Intersectia is the Romanian term for the concept of intersection, used across mathematics and related fields. In general, it denotes the set or region of elements that are common to two or more objects, such as sets, lines, curves, or regions.

In set theory and algebra, the intersection A ∩ B consists of all elements that belong to both A and B. The operation is commutative and associative: A ∩ B = B ∩ A and A ∩ (B ∩ C) = (A ∩ B) ∩ C. The universal set U acts as an identity for intersection: A ∩ U = A. For an indexed family of sets {A_i}, the intersection ∩i A_i contains elements present in every A_i. Intersections distribute over unions: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C). De Morgan’s laws relate intersections to unions and complements.

In geometry, the intersection of two lines in a plane is a single point if the lines are not parallel, is the entire line if they coincide, or is empty if they are parallel. The intersection of curves can yield one or more points, or none, depending on their shapes and positions.

In topology and analysis, intersections are used to describe common points of sets such as open or closed sets. Finite intersections of open sets are open, but arbitrary (infinite) intersections of open sets need not be open; for example, the intersection of the intervals (-1/n, 1/n) for n = 1, 2, 3, … is {0}.

Beyond mathematics, intersectia appears in urban planning as road or street crossings, and in computer science as an operation on data structures or bitsets. See also Union and Set theory.