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.)
“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)
“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)