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)
“What shall we say who have knowledge
Carried to the heart? Shall we take the act
To the grave? Shall we, more hopeful, set up the grave
In the house? The ravenous grave?”
—Allen Tate (1899–1979)
“Don’t confuse hypothesis and theory. The former is a possible explanation; the latter, the correct one. The establishment of theory is the very purpose of science.”
—Martin H. Fischer (1879–1962)