intersection,
n. 1. (Geometry) a point or set of points common to two or more figures.
2. also called (archaic) product. (Set theory) a. the set of elements that are members of two or more given sets, written S ∩ T or ∩ i Si, often read as cap. In the following Venn diagram the sets S and T are represented by the regions shaded respectively vertically and horizontally; their intersection is the region shaded in both directions.
S ∩ T is cross-hatched.
b. the binary operation that forms such a set from two given sets.
c. more generally, the intersection over any collection of subsets
C = {Cα : α ∈ A}
of a given set X is the set of which the elements lie in each member of the collection. This is denoted
∩ α∈A Cα
or ∩ C. If the collection of subsets is empty, ∩ ∅ = X while ∪ ∅ = ∅; so, to avoid the seeming paradox that the intersection is not contained in the union it is sometimes useful to replace the universe X by ∪C before computing the intersection denoted ∩*. This only changes the intersection over an empty collection and ensures that ∩*C is always a subset of ∪C.
b. the binary operation that forms such a set from two given sets.
c. more generally, the intersection over any collection of subsets
C = {Cα : α ∈ A}
of a given set X is the set of which the elements lie in each member of the collection. This is denoted
∩ α∈A Cα
or ∩ C. If the collection of subsets is empty, ∩ ∅ = X while ∪ ∅ = ∅; so, to avoid the seeming paradox that the intersection is not contained in the union it is sometimes useful to replace the universe X by ∪C before computing the intersection denoted ∩*. This only changes the intersection over an empty collection and ensures that ∩*C is always a subset of ∪C.