Elementary Facts on Cardinal Numbers
摘要
Two sets A and B are called equinumerous if there exists a bijection from A onto B. In this case, the notation \(A \sim B\) is often used. The relation \(R(A,B)\) defined by \(A \sim B\) is reflexive, symmetric, and transitive, i.e., one has \(\displaystyle R(A,A),\qquad R(A,B) \Rightarrow R(B,A),\qquad (R(A,B)~\&~R(B,C)) \Rightarrow R(A,C) \) for any sets A, B, and C. This fact is easily verified.