- Importance: languages are sets
- A
*set*is a collection of "things," called the*elements*or*members*of the set. It is essential to have a criterion for determining, for any given thing, whether it is or is not a member of the given set. This criterion is called the*membership criterion*of the set. - There are two common ways of indicating the members of a set:
- List all the elements, e.g. {a, e, i, o, u}
- Provide some sort of an algorithm or rule, such as a grammar

- Notation:
- To indicate that x is a member of set S, we write x S
- We denote the
*empty set*(the set with no members) as {} or - If every element of set A is also an element of set B, we say that A
is a
*subset*of B, and write A B - If every element of set A is also an element of set B, but B also has some
elements not contained in A, we say that A is a
*proper subset*of B, and write A B

Copyright © 1996 by David Matuszek

Last modified Feb 2, 1996