"Distributivity" redirects here. Not to be confused with Distributivism.
Distributive property
Visualization of distributive law for positive numbers
Type
Law, rule of replacement
Field
Elementary algebra
Boolean algebra
Abstract algebra
Set theory
Propositional calculus
Symbolic statement
Elementary algebra
Propositional calculus:
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
Therefore, one would say that multiplication distributes over addition.
This basic property of numbers is part of the definition of most algebraic structures that have two operations called addition and multiplication, such as complex numbers, polynomials, matrices, rings, and fields. It is also encountered in Boolean algebra and mathematical logic, where each of the logical and (denoted ) and the logical or (denoted ) distributes over the other.
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In mathematics, the distributiveproperty of binary operations is a generalization of the distributive law, which asserts that the equality x ⋅ ( y + z...
word, was coined), in a 1982 paper by Sergei Matveev (under the name distributive groupoids) and in a 1986 conference paper by Egbert Brieskorn (where...
Distributive may refer to: Distributiveproperty, in algebra, logic and mathematics Distributive pronoun and distributive adjective (determiner), in linguistics...
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Möbius function. Completely multiplicative functions also satisfy a distributive law. If f is completely multiplicative then f ⋅ ( g ∗ h ) = ( f ⋅ g )...
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the properties of the arithmetic operations (commutative properties and associative properties of addition and multiplication, distributiveproperty and...
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a power of 3 (exponent of 1/3) Properties of Operations Associative propertyDistributiveproperty Commutative property Factorial – Multiplication of numbers...
In mathematics, a distributive lattice is a lattice in which the operations of join and meet distribute over each other. The prototypical examples of such...
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c+3c^{2}a+3c^{2}b+6abc.} This can be computed by hand using the distributiveproperty of multiplication over addition, but it can also be done (perhaps...
y ⋅ z ) . {\displaystyle (x\cdot y)\cdot z=x\cdot (y\cdot z).} Distributiveproperty Holds with respect to multiplication over addition. This identity...
equivalently A(u + v) = λ(u + v). This can be checked using the distributiveproperty of matrix multiplication. Similarly, because E is a linear subspace...
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= A ∩ ( B ∩ C ) {\displaystyle (A\cap B)\cap C=A\cap (B\cap C)} Distributiveproperty: A ∪ ( B ∩ C ) = ( A ∪ B ) ∩ ( A ∪ C ) {\displaystyle A\cup (B\cap...
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