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In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality ...
The FOIL method is a special case of a more general method for multiplying algebraic expressions using the distributive law. The word FOIL was originally intended solely as a mnemonic for high-school students learning algebra. The term appears in William Betz's 1929 text Algebra for Today, where he states: [2]
The principle of distributivity states that the algebraic distributive law is valid, where both logical conjunction and logical disjunction are distributive over each other so that for any propositions A, B and C the equivalences
Thus any distributive meet-semilattice in which binary joins exist is a distributive lattice. A join-semilattice is distributive if and only if the lattice of its ideals (under inclusion) is distributive. [1] This definition of distributivity allows generalizing some statements about distributive lattices to distributive semilattices.
The generalized distributive law (GDL) is a generalization of the distributive property which gives rise to a general message passing algorithm. [1] It is a synthesis of the work of many authors in the information theory, digital communications, signal processing, statistics, and artificial intelligence communities.
In category theory, an abstract branch of mathematics, distributive laws between monads are a way to express abstractly that two algebraic structures distribute one over the other. Suppose that ( S , μ S , η S ) {\displaystyle (S,\mu ^{S},\eta ^{S})} and ( T , μ T , η T ) {\displaystyle (T,\mu ^{T},\eta ^{T})} are two monads on a category C .
Galileo's law of odd numbers. A ramification of the difference of consecutive squares, Galileo's law of odd numbers states that the distance covered by an object falling without resistance in uniform gravity in successive equal time intervals is linearly proportional to the odd numbers. That is, if a body falling from rest covers a certain ...
(A, ≤) is a bounded partial order with a least upper bound and greatest lower bound for every pair of elements, and the meet and join operations so defined satisfy the distributive law, then the complementation can also be defined as an involutive anti-automorphism, that is, a structure A = (A, ≤, ¬) such that: