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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]
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 ...
In a non-distributive lattice, there may be elements that are distributive, but not dual distributive (and vice versa). For example, in the depicted pentagon lattice N 5, the element x is distributive, [2] but not dual distributive, since x ∧ (y ∨ z) = x ∧ 1 = x ≠ z = 0 ∨ z = (x ∧ y) ∨ (x ∧ z).
Distributivity, a property of binary operations that generalises the distributive law from elementary algebra; Distribution (number theory) Distribution problems, a common type of problems in combinatorics where the goal is to enumerate the number of possible distributions of m objects to n recipients, subject to various conditions; see ...
For example, if a sequence is equidistributed in [0, 2], since the interval [0.5, 0.9] occupies 1/5 of the length of the interval [0, 2], as n becomes large, the proportion of the first n members of the sequence which fall between 0.5 and 0.9 must approach 1/5. Loosely speaking, one could say that each member of the sequence is equally likely ...
The Hadamard product operates on identically shaped matrices and produces a third matrix of the same dimensions. In mathematics, the Hadamard product (also known as the element-wise product, entrywise product [1]: ch. 5 or Schur product [2]) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding elements.
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1.000 2 ×2 0 + (1.000 2 ×2 0 + 1.000 2 ×2 4) = 1.000 2 ×2 0 + 1.000 2 ×2 4 = 1.00 0 2 ×2 4 Even though most computers compute with 24 or 53 bits of significand, [ 8 ] this is still an important source of rounding error, and approaches such as the Kahan summation algorithm are ways to minimise the errors.
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