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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]
Developed in 1990 by Ross Quinlan, [1] FOIL learns function-free Horn clauses, a subset of first-order predicate calculus.Given positive and negative examples of some concept and a set of background-knowledge predicates, FOIL inductively generates a logical concept definition or rule for the concept.
The term "FOIL rule" is rarely used, "FOIL method" is an order of magnitude more common. I suggest moving the article accordingly. -- Vaughan Pratt ( talk ) 19:04, 6 September 2009 (UTC) [ reply ]
For any pair of positive integers n and k, the number of k-tuples of positive integers whose sum is n is equal to the number of (k − 1)-element subsets of a set with n − 1 elements. For example, if n = 10 and k = 4, the theorem gives the number of solutions to x 1 + x 2 + x 3 + x 4 = 10 (with x 1, x 2, x 3, x 4 > 0) as the binomial coefficient
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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".