Naive Set Theory (book)
Encyclopedia
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 axiom
s, 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.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
textbook by Paul Halmos
Paul Halmos
Paul Richard Halmos was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis . He was also recognized as a great mathematical expositor.-Career:Halmos obtained his B.A...
originally published in 1960. This book is an undergraduate introduction to not-very-naive set theory
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
. 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 axiom
Axiom
In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...
s, the book does introduce all the axioms of Zermelo–Fraenkel set theory
Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory with the axiom of choice, named after mathematicians Ernst Zermelo and Abraham Fraenkel and commonly abbreviated ZFC, is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets without the paradoxes...
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.