Multiplication of ordinal numbers, in contrast, is only left-distributive, not right-distributive. The cross product is left- and right-distributive over vector addition, though not commutative. The union of sets is distributive over intersection, and intersection is distributive over union. Logical disjunction ("or") is distributive over logical conjunction ("and"), and vice versa. For real numbers (and for any totally ordered set), the maximum operation is distributive over the minimum operation, and vice versa: For integers, the greatest common divisor is distributive over the least common multiple, and vice versa: For real numbers, addition distributes over the maximum operation, and also over the minimum operation: For binomial multiplication, distribution is sometimes referred to as the FOIL MethodKim Steward (2011) Multiplying Polynomials from Virtual Math Lab at West Texas A&M University (First terms Outer Inner and Last ) such as: In all semirings, including the complex numbers, the quaternions, polynomials, and matrices, multiplication distributes over addition: In all algebras over a field, including the octonions and other non-associative algebras, multiplication distributes over addition.
multiplication of ordinal numbers in contrast is only left-distributive not right-distributive the cross product is left- and right-distributive over vector addition though not commutative the union of sets is distributive over intersection and intersection is distributive over union logical disjunction ("or") is distributive over logical conjunction ("and") and vice versa for real numbers (and for any totally ordered set) the maximum operation is distributive over the minimum operation and vice versa for integers the greatest common divisor is distributive over the least common multiple and vice versa for real numbers addition distributes over the maximum operation and also over the minimum operation for binomial multiplication distribution is sometimes referred to as the foil methodkim steward (2011) multiplying polynomials from virtual math lab at west texas a&m university (first terms outer inner and last ) such as in all semirings including the complex numbers the quaternions polynomials and matrices multiplication distributes over addition in all algebras over a field including the octonions and other non-associative algebras multiplication distributes over addition