<Dd> c c = (2 א 0) c = 2 c × א 0 = 2 c . (\ displaystyle (\ mathfrak (c)) ^ (\ mathfrak (c)) = \ left (2 ^ (\ aleph _ (0)) \ right) ^ (\ mathfrak (c)) = 2 ^ ((\ mathfrak (c)) \ times \ aleph _ (0)) = 2 ^ (\ mathfrak (c)).) </Dd> <Ul> <Li> If X = (a, b, c) and Y = (apples, oranges, peaches), then X = Y because ((a, apples), (b, oranges), (c, peaches)) is a bijection between the sets X and Y . The cardinality of each of X and Y is 3 . </Li> <Li> If X <Y, then there exists Z such that X = Z and Z ⊆ Y . </Li> <Li> If X ≤ Y and Y ≤ X, then X = Y . This holds even for infinite cardinals, and is known as Cantor--Bernstein--Schroeder theorem . </Li> <Li> Sets with cardinality of the continuum </Li> </Ul> <Li> If X = (a, b, c) and Y = (apples, oranges, peaches), then X = Y because ((a, apples), (b, oranges), (c, peaches)) is a bijection between the sets X and Y . The cardinality of each of X and Y is 3 . </Li> <Li> If X <Y, then there exists Z such that X = Z and Z ⊆ Y . </Li>

How to write the number of elements in a set