Free Universal Algebras
Let be any set, let be an algebraic structure of type generated by . Let the underlying set of this algebraic structure, sometimes called universe, be, and let be a function. We say that, (or informally just ) is a free algebra (of type ) on the set of free generators if, for every algebra of type and function, where is a universe of, there exists a unique homomorphism such that .
Read more about this topic: Free Object
Famous quotes containing the words free and/or universal:
“It is among the ranks of school-age children, those six- to twelve-year-olds who once avidly filled their free moments with childhood play, that the greatest change is evident. In the place of traditional, sometimes ancient childhood games that were still popular a generation ago, in the place of fantasy and make- believe play . . . today’s children have substituted television viewing and, most recently, video games.”
—Marie Winn (20th century)
“Vanity, or to call it by a gentler name, the desire of admiration and applause, is, perhaps, the most universal principle of human actions.... Where that desire is wanting, we are apt to be indifferent, listless, indolent, and inert.... I will own to you, under the secrecy of confession, that my vanity has very often made me take great pains to make many a woman in love with me, if I could, for whose person I would not have given a pinch of snuff.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)