# Category:Definitions/Sets

This category contains definitions related to Sets.

Related results can be found in Category:Sets.

A **set** is intuitively defined as any aggregation of objects, called elements, which can be precisely defined in some way or other.

We can think of each set as a single entity in itself, and we can denote it (and usually do) by means of a single symbol.

That is, *anything you care to think of* can be a set. This concept is known as the Axiom of Abstraction.

However, there are problems with the Axiom of Abstraction. If we allow it to be used without any restrictions at all, paradoxes arise, the most famous example probably being Russell's Paradox.

Hence some sources define a **set** as a ** 'well-defined' collection of objects**, leaving the concept of what constitutes well-definition to later in the exposition.

## Pages in category "Definitions/Sets"

The following 24 pages are in this category, out of 24 total.

### S

- Definition:Set
- Definition:Set Definition by Predicate
- Definition:Set Definition by Predicate/Also known as
- Definition:Set-Builder Notation
- Definition:Set/Also known as
- Definition:Set/Definition by Predicate
- Definition:Set/Distinction between Element and Set
- Definition:Set/Explicit Set Definition
- Definition:Set/Implicit Set Definition
- Definition:Set/Implicit Set Definition/Infinite Set
- Definition:Set/Implicit Set Definition/Multipart Infinite Set
- Definition:Set/Point Set
- Definition:Set/Uniqueness of Elements
- Definition:Set/Uniqueness of Elements/Equality of Sets
- Definition:Set/Uniqueness of Elements/Multiple Specification
- Definition:Set/Uniqueness of Elements/Order of Listing