Elementary Facts on Cardinal Numbers

Alexander Kharazishvili
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Alexander Kharazishvili: Tbilisi State University, Andrea Razmadze Mathematical Institute

Chapter Chapter 3 in Lectures on Real-valued Functions, 2025, pp 23-36 from Springer

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

Date: 2025
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DOI: 10.1007/978-3-031-95369-9_3

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