page_title: Set
section_title: Subsets
hierarchical_section_title: Set / What to do with sets / Subsets
context_page_description: A set is an idea from mathematics. A set has members. A set is fixed by its members, so any two sets with the same members must be same. A set cannot have the same member more than once. Membership is the only thing that means anything. For example, there is no order or other distinction among the members. One particular set is the "empty set". The empty set has no members. Anything can be a member of a set, including sets themselves.
context_section_description: If you look at the set {a,b} and the set {a,b,c,d}, you can see that all elements in the first set are also in the second set.
   We say: {a,b} is a subset of {a,b,c,d}
  
  As a formula it looks like this:
  In general, when all elements of A are also elements of B, we call A a subset of B:
  
  It is usually read "A is contained in B"
  Example:
  
  Every Chevrolet is an American car. So the set of all Chevrolets is contained in the set of all American cars.
caption: A
          ⊆
          B
        
      
      {\displaystyle A\subseteq B}