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)
“Such a set of tittle tattle, prittle prattle visitants! Oh Dear! I am so sick of the ceremony and fuss of these fall lall people! So much dressing—chitchat—complimentary nonsense—In short, a country town is my detestation. All the conversation is scandal, all the attention, dress, and almost all the heart, folly, envy, and censoriousness.”
—Frances Burney (1752–1840)
“The weakness of the man who, when his theory works out into a flagrant contradiction of the facts, concludes “So much the worse for the facts: let them be altered,” instead of “So much the worse for my theory.””
—George Bernard Shaw (1856–1950)