1. Two infinite sets \(A\) and \(B\) have the same Cardinality (that is, \(\left A \right = \left B \right\)) if there exists a bijection \(A \to B.\) This bijection-based

2. 21 In Seam parlance, this action is called bijection, short for bidirectional injection.

3. Seam cleverly uses bijection to allow data to flow in and out of each page of a "Web conversation" in a new, declarative manner.

4. The image of a left Coset under the mapping is the right Coset .This mapping induces a bijection from the set of left Cosets of to the set of right Cosets of .

5. 2005, Johan de Jong, “Set Theory”, in The Stacks Project‎[1], retrieved 2018-2-26: The Cardinality of a set A is the least ordinal α such that there exists a bijection between A and α

6. Specifically, let be a group, and let be a subgroup of .The left Cosets modulo are the subsets of of the form , for .Note that for any Coset , the mapping is a bijection from to .Hence for any , .