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  2. Distributive property - Wikipedia

    en.wikipedia.org/wiki/Distributive_property

    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 ...

  3. FOIL method - Wikipedia

    en.wikipedia.org/wiki/FOIL_method

    In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials [1] —hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product: The general form is. Note that a is both a "first" term and an "outer" term; b is both a "last" and "inner" term, and so forth.

  4. Commutative property - Wikipedia

    en.wikipedia.org/wiki/Commutative_property

    In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a property of arithmetic, e.g. "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more ...

  5. Exterior algebra - Wikipedia

    en.wikipedia.org/wiki/Exterior_algebra

    Formal definition. The exterior algebra of a vector space over a field is defined as the quotient algebra of the tensor algebra by the two-sided ideal generated by all elements of the form such that . [6] Symbolically, The exterior product of two elements of is defined by.

  6. Function composition - Wikipedia

    en.wikipedia.org/wiki/Function_composition

    Properties. The composition of functions is always associative —a property inherited from the composition of relations. [1] That is, if f, g, and h are composable, then f ∘ (g ∘ h) = (f ∘ g) ∘ h. [2] Since the parentheses do not change the result, they are generally omitted.

  7. Algebra of sets - Wikipedia

    en.wikipedia.org/wiki/Algebra_of_sets

    Fundamentals. The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".

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