Bézout's Theorem

A result in algebraic geometry stating that, over an algebraically closed field, two projective plane curves without a common component intersect in a number of points equal to the product of their degrees, counted with multiplicity and including intersections at infinity.

A statement in algebraic geometry that two projective plane algebraic curves without a common component intersect in a number of points counted with multiplicity equal to the product of their degrees, over an algebraically closed field.