Search results
Results from the WOW.Com Content Network
2.1 Distributive properties. 2.2 First ... where i, j, and k are the unit vectors for the x-, y-, and z-axes, respectively. As the name implies the curl is a measure ...
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 2 ⋅ ( 1 + 3 ) = ( 2 ⋅ 1 ) + ( 2 ⋅ 3 ) . {\displaystyle 2\cdot (1+3)=(2\cdot 1)+(2\cdot 3).}
The map φ defined by φ(y) = x ∨ y is a lattice homomorphism from L to the upper closure ↑x = { y ∈ L: x ≤ y}; The binary relation Θ x on L defined by y Θ x z if x ∨ y = x ∨ z is a congruence relation, that is, an equivalence relation compatible with ∧ and ∨. [3] In an arbitrary lattice, if x 1 and x 2 are distributive ...
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]
[2] The cross product is anticommutative (that is, a × b = − b × a) and is distributive over addition, that is, a × (b + c) = a × b + a × c. [1] The space together with the cross product is an algebra over the real numbers, which is neither commutative nor associative, but is a Lie algebra with the cross product being the Lie bracket.
Let X # denote the algebraic dual space of an R-module X. Let X and Y be R-modules. If u : X → Y is a linear map, then its algebraic adjoint or dual, [8] is the map u # : Y # → X # defined by f ↦ f ∘ u. The resulting functional u # (f) is called the pullback of f by u. The following relation characterizes the algebraic adjoint of u [9 ...
For example, taking the statement x + 1 = 0, if x is substituted with 1, this implies 1 + 1 = 2 = 0, which is false, which implies that if x + 1 = 0 then x cannot be 1. If x and y are integers, rationals, or real numbers, then xy = 0 implies x = 0 or y = 0. Consider abc = 0. Then, substituting a for x and bc for y, we learn a = 0 or bc = 0.
Visual proof of the Pythagorean identity: for any angle , the point (,) = (, ) lies on the unit circle, which satisfies the equation + =.Thus, + =. In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables ...