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:
““The days have outnumbered
my fingers and toes.
What can I count with now?”
Saying this,
the naive girl cries.”
—Hla Stavhana (c. 50 A.D.)
“Whoever wants to set a good example must add a grain of foolishness to his virtue: then others can imitate and yet at the same time surpass the one they imitate—which human beings love to do.”
—Friedrich Nietzsche (1844–1900)
“... the first reason for psychology’s failure to understand what people are and how they act, is that clinicians and psychiatrists, who are generally the theoreticians on these matters, have essentially made up myths without any evidence to support them; the second reason for psychology’s failure is that personality theory has looked for inner traits when it should have been looking for social context.”
—Naomi Weisstein (b. 1939)