From ProofWiki
Jump to navigation Jump to search

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.