A naive theory in the sense of "naive set theory" is a non-formalized theory, that is, a theory that uses natural language to describe sets and … See more

The simplest way to describe a set is to list its elements between curly braces (known as defining a set extensionally). Thus {1, 2} denotes the set whose only elements are 1 and 2. (See See more

In certain contexts, one may consider all sets under consideration as being subsets of some given universal set. For instance, when investigating … See more

Intuitively, an ordered pair is simply a collection of two objects such that one can be distinguished as the first element and the other as the … See more

In naive set theory, a set is described as a well-defined collection of objects. These objects are called the elements or members of the set. Objects can be anything: numbers, … See more

Given two sets A and B, A is a subset of B if every element of A is also an element of B. In particular, each set B is a subset of itself; a subset of B … See more

Given two sets A and B, their union is the set consisting of all objects which are elements of A or of B or of both (see axiom of union). … See more