Distributive Property - Definition

Definition

Given a set S and two binary operators · and + on S, we say that the operation ·

  • is left-distributive over + if, given any elements x, y, and z of S,
x · (y + z) = (x · y) + (x · z);
  • is right-distributive over + if, given any elements x, y, and z of S:
(y + z) · x = (y · x) + (z · x);
  • is distributive over + if it is left- and right-distributive.

Notice that when · is commutative, then the three above conditions are logically equivalent.

Read more about this topic:  Distributive Property

Famous quotes containing the word definition:

    The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.
    Samuel Taylor Coleridge (1772–1834)

    The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.
    William James (1842–1910)

    ... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.
    Adrienne Rich (b. 1929)