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.

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Elementary Facts on Cardinal Numbers

  • Alexander Kharazishvili

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.