Naive set theory is one of several theories of sets used in the discussion of the foundations of mathematics. The informal content of this naive set theory supports both the aspects of mathematical sets familiar in discrete mathematics (for example Venn diagrams and symbolic reasoning about their Boolean algebra), and the everyday usage of set theory concepts in most contemporary mathematics.
Sets are of great importance in mathematics; in fact, in modern formal treatments, most mathematical objects (numbers, relations, functions, etc.) are defined in terms of sets. Naive set theory can be seen as a stepping-stone to more formal treatments, and suffices for many purposes.
Read more about Naive Set Theory: Requirements, Sets, Membership and Equality, Specifying Sets, Subsets, Universal Sets and Absolute Complements, Unions, Intersections, and Relative Complements, Ordered Pairs and Cartesian Products, Some Important Sets, Paradoxes
Famous quotes containing the words naive, set and/or theory:
“Cynicism is full of naive disappointments.”
—Mason Cooley (b. 1927)
“Genghis Khan, in his usual jodhpurs accessorized with whip, straddled a canvas chair and gloated upon the fairyland he had built. Journalists, photographers, secretaries, sycophants, script girls, and set dressers milled and stirred around him, activity ... irresistibly reminiscent of the movement of maggots upon rotting meat.”
—Angela Carter (1940–1992)
“No one thinks anything silly is suitable when they are an adolescent. Such an enormous share of their own behavior is silly that they lose all proper perspective on silliness, like a baker who is nauseated by the sight of his own eclairs. This provides another good argument for the emerging theory that the best use of cryogenics is to freeze all human beings when they are between the ages of twelve and nineteen.”
—Anna Quindlen (20th century)