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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. For example, in elementary arithmetic , one has 2 ⋅ ( 1 + 3 ) = ( 2 ⋅ 1 ) + ( 2 ⋅ 3 ) . {\displaystyle 2\cdot (1+3)=(2\cdot 1)+(2\cdot 3).}
These constructs surfaced again in the 1980s: in a 1982 paper by David Joyce [5] (where the term quandle, an arbitrary nonsense word, was coined), [6] in a 1982 paper by Sergei Matveev (under the name distributive groupoids) [7] and in a 1986 conference paper by Egbert Brieskorn (where they were called automorphic sets). [8]
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]
Mathematically, the ability to break up a multiplication in this way is known as the distributive law, which can be expressed in algebra as the property that a(b+c) = ab + ac. The grid method uses the distributive property twice to expand the product, once for the horizontal factor, and once for the vertical factor.
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 ...
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 .
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