Search results
Results From The WOW.Com Content Network
In approximate arithmetic, such as floating-point arithmetic, the distributive property of multiplication (and division) over addition may fail because of the limitations of arithmetic precision. For example, the identity 1 / 3 + 1 / 3 + 1 / 3 = ( 1 + 1 + 1 ) / 3 {\displaystyle 1/3+1/3+1/3=(1+1+1)/3} fails in decimal arithmetic , regardless of ...
The proof of the factorization identity is straightforward. Starting from the right-hand side, apply the distributive law to get (+) = +By the commutative law, the middle two terms cancel:
The great variety and (relative) complexity of formulas involving set subtraction (compared to those without it) is in part due to the fact that unlike ,, and , set subtraction is neither associative nor commutative and it also is not left distributive over ,, , or even over itself.
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]
An element x is called a dual distributive element if ∀y,z: x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z). In a distributive lattice, every element is of course both distributive and dual distributive. In a non-distributive lattice, there may be elements that are distributive, but not dual distributive (and vice versa).
For example, a basic property of addition is commutativity which states that the order of numbers being added together does not matter. Commutativity is stated algebraically as ( a + b ) = ( b + a ) {\displaystyle (a+b)=(b+a)} .
In mathematics, a category is distributive if it has finite products and finite coproducts and such that for every choice of objects,,, the canonical map [,]: + (+)is an isomorphism, and for all objects , the canonical map is an isomorphism (where 0 denotes the initial object).
In mathematics, a property is any characteristic that applies to a given set. [1] Rigorously, a property p defined for all elements of a set X is usually defined as a function p: X → {true, false}, that is true whenever the property holds; or, equivalently, as the subset of X for which p holds; i.e. the set {x | p(x) = true}; p is its indicator function.