Naive Set Theory is a mathematics textbook by Paul Halmos originally published in 1960. This book is an undergraduate introduction to not-very-naive set theory. It is still considered by many to be the best introduction to set theory for beginners. While the title states that it is naive, which is usually taken to mean without axioms, the book does introduce all the axioms of Zermelo–Fraenkel set theory and gives correct and rigorous definitions for basic objects. Where it differs from a "true" axiomatic set theory book is its character: there are no long-winded discussions of axiomatic minutiae, and there is next to nothing about advanced topics like large cardinals. Instead, it tries to be intelligible to someone who has never thought about set theory before.
Famous quotes containing the words naive, set and/or theory:
“Cynicism is full of naive disappointments.”
—Mason Cooley (b. 1927)
“Unfortunately, many things have been omitted which should have been recorded in our journal; for though we made it a rule to set down all our experiences therein, yet such a resolution is very hard to keep, for the important experience rarely allows us to remember such obligations, and so indifferent things get recorded, while that is frequently neglected. It is not easy to write in a journal what interests us at any time, because to write it is not what interests us.”
—Henry David Thoreau (1817–1862)
“A theory of the middle class: that it is not to be determined by its financial situation but rather by its relation to government. That is, one could shade down from an actual ruling or governing class to a class hopelessly out of relation to government, thinking of gov’t as beyond its control, of itself as wholly controlled by gov’t. Somewhere in between and in gradations is the group that has the sense that gov’t exists for it, and shapes its consciousness accordingly.”
—Lionel Trilling (1905–1975)