
related topics 
{math, number, function} 
{theory, work, human} 
{group, member, jewish} 
{specie, animal, plant} 

Naive set theory is one of several theories of sets used in the discussion of the foundations of mathematics.^{[1]} 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 steppingstone to more formal treatments, and suffices for many purposes.
Contents
Requirements
In the sense of this article, a naive theory is a nonformalized theory, that is, a theory that uses a natural language to describe sets. The words and, or, if ... then, not, for some, for every are not subject to rigorous definition. It is useful to study sets naively at an early stage of mathematics in order to develop facility for working with them. Furthermore, a firm grasp of set theoretical concepts from a naive standpoint is important as a first stage in understanding the motivation for the formal axioms of set theory.
This article develops a naive theory. Sets are defined informally and a few of their properties are investigated. Links in this article to specific axioms of set theory describe some of the relationships between the informal discussion here and the formal axiomatization of set theory, but no attempt is made to justify every statement on such a basis. The first development of set theory was a naive set theory. It was created at the end of the 19th century by Georg Cantor as part of his study of infinite sets.
Full article ▸


related documents 
Inverse function 
Finite field 
Peano axioms 
Limit superior and limit inferior 
Recursion 
Word problem for groups 
Cantor set 
Matrix multiplication 
Zermeloâ€“Fraenkel set theory 
Inner product space 
Computational complexity theory 
Markov chain 
Topological space 
Collatz conjecture 
Addition 
Pythagorean theorem 
Mathematical induction 
Wavelet 
Hash table 
Recurrence relation 
Braket notation 
Groupoid 
Cauchy sequence 
Pi 
Binary search tree 
Forcing (mathematics) 
Elliptic curve cryptography 
Johnston diagram 
Nonstandard analysis 
Principal components analysis 
