Closure

A Set is closed under a binary operation if any two elements of the set when combined using the binary operation produce an element of the same set. Thus a set A is closed under the binary operation * if for all a and b $\in\$ A then a * b $\in\$ A. This idea extends beyond simple binary operations.

For example:

The set of natural numbers is closed under addition and multiplication

but not closed under subtraction.

The set of the integers is closed under addition, subtraction and multiplication

but not under division

Some counter-examples:

The set of rational numbers is not closed under minimum upper bound
The set of real numbers is not closed under square roots

Last change to this page
Full Page history
Links to this page

Edit this page
(with sufficient authority)
Change password

Recent changes
All pages
Search