# Naive Set Theory

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.

### 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.)

Anyone who seeks for the true causes of miracles, and strives to understand natural phenomena as an intelligent being, and not to gaze at them like a fool, is set down and denounced as an impious heretic by those, whom the masses adore as the interpreters of nature and the gods. Such persons know that, with the removal of ignorance, the wonder which forms their only available means for proving and preserving their authority would vanish also.
Baruch (Benedict)

... liberal intellectuals ... tend to have a classical theory of politics, in which the state has a monopoly of power; hoping that those in positions of authority may prove to be enlightened men, wielding power justly, they are natural, if cautious, allies of the “establishment.”
Susan Sontag (b. 1933)