## Types of Sets

•  Cardinality of Set X:

• n(X), Set X contains n(X) elements

• Empty:

• holds no elements

• { }, Ø, n(X) = 0, |A| = 0

• Equal:

• two sets that contain the same elements, and no other elements

• =, X = Y, Set X is equal to Set Y

• Equivalent:

• two sets not necessarily having the same elements, while having the same number of elements (the same cardinality)

• n(X) = n(Y), Set X is equivalent to Set Y; ≈ , X ≈ Y

• Finite:

• holds a number of elements that is limited and countable

• Improper Subset:

• a set that is exactly the same as itself

• Infinite:

• holds a number of elements that is unlimited and uncountable

• ∞, n(X) = ∞

• Null:

• also known as the empty set – the set that holds no elements

• { }, Ø, n(X) = 0, |A| = 0

• Proper Subset:

• a set X that contains only elements of set Y but does not contain at least one element of Y

• ⊂, X ⊂ Y, Set X is a proper subset of Set Y

• Proper Superset:

• set X holds all elements of set Y but is not equal to Y

• ⊃, X ⊃ Y, Set X is a proper superset of Set Y

• Power:

• holds all subsets of a given set

• P, X = P(Y), Set X contains all the subsets of Set Y

• Singleton:

• holds only one element, no more and no less

• Subset:

• a set X that contains only elements of set Y

• ⊆, X ⊆ Y, Set X is a subset of Set Y

• Superset:

• set X contains all elements of set Y, and only elements of Y

• ⊇, X ⊇ Y, Set X is a superset of Set Y

• Universal:

• holds all elements of all other sets under consideration

• U, X = U, Set X is the universal set