Closure
From AoPSWiki
Closure is a property of an abstract algebraic structure, such as a set, group, ring, or field
Definition
An algebraic structure 
is said to have closure in a binary operation 
if for any 
, 
. In words, when any two members of are combined using the operation, the result also is a member of .
Examples
- The real number system
has closure in addition, subtraction, multiplication, division, exponentiation, and also higher level operations such as 
.
- The rational number system
has closure in addition, subtraction, multiplication, and division
- The natural and whole number systems
have closure in addition and multiplication.
- The complex number system
has closure in addition, subtraction, multiplication, division, exponentiation, and also higher level operations such as .
- The integral number system
has closure in addition, subtraction, multiplication, and exponentiation.
