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In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality (+) = + is always true in elementary algebra.
A lattice (L,∨,∧) is distributive if the following additional identity holds for all x, y, and z in L: x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z). Viewing lattices as partially ordered sets, this says that the meet operation preserves non-empty finite joins. It is a basic fact of lattice theory that the above condition is equivalent to its ...
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.
In the mathematical area of order theory, a completely distributive lattice is a complete lattice in which arbitrary joins distribute over arbitrary meets.. Formally, a complete lattice L is said to be completely distributive if, for any doubly indexed family {x j,k | j in J, k in K j} of L, we have
Distributive justice concerns the socially just allocation of resources, goods, opportunity in a society.It is concerned with how to allocate resources fairly among members of a society, taking into account factors such as wealth, income, and social status.
A homomorphism μ : S → T between join-semilattices S and T is weakly distributive, if for all a, b in S and all c in T such that μ(c) ≤ a ∨ b, there are elements x and y of S such that c ≤ x ∨ y, μ(x) ≤ a, and μ(y) ≤ b. Examples:
Taylor Swift topped the chart for seven weeks with three different albums in 2023; one of them, 1989 (Taylor's Version), became the best selling album of the year.. This is a list of the albums ranked number one in the United States during 2023.