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:
“It would be naive to think that peace and justice can be achieved easily. No set of rules or study of history will automatically resolve the problems.... However, with faith and perseverance,... complex problems in the past have been resolved in our search for justice and peace. They can be resolved in the future, provided, of course, that we can think of five new ways to measure the height of a tall building by using a barometer.”
—Jimmy Carter (James Earl Carter, Jr.)
“[T]he dignity of parliament it seems can brook no opposition to it’s power. Strange that a set of men who have made sale of their virtue to the minister should yet talk of retaining dignity!”
—Thomas Jefferson (1743–1826)
“Osteopath—One who argues that all human ills are caused by the pressure of hard bone upon soft tissue. The proof of his theory is to be found in the heads of those who believe it.”
—H.L. (Henry Lewis)