Subset

In set theory, a set  is called a subset of a set  if all of the elements of  are contained in . For example, any set is a subset of itself. Another example of a subset is a proper subset: a set  is called a proper subset of a set  if  is subset of  but is not equal to .
The symbol "" always means "is a subset of." The symbol "" always means "is a proper subset of." There is also the symbol "", which some authors use to mean "is a subset of" and other authors only use to mean "is a proper subset of."

For example:
 is a subset of , so we could write .

 is a proper subset of , so we could write ,, or .

The interval [0, 1] is a proper subset of the set of real numbers , so .

 Related pages 

 Subset sum problem
 Vector subspace

 References 

Category:Set theory