Mathematical Reasoning: Writing and Proof (PreTeXt Edition)

Equivalent sets

Sets with the same cardinality

Finite set

Infinite set

Cardinality of a finite set

Cardinality of $\mathbb{N}$

${\mathrm{\aleph }}_0$

Countably infinite set

Denumerable set

Uncountable set

Theorem 9.3

Theorem 9.6

Corollary 9.8

Theorem 9.9 [The Pigeonhole Principle]

Theorem 9.11

Theorem 9.14

Theorem 9.15

Theorem 9.18

Theorem 9.20

Theorem 9.21

Theorem 9.22

Corollary 9.23

Theorem 9.27

Theorem 9.29

Theorem 9.31

Theorem 9.32 [Cantor's Theorem]

Corollary 9.33

Theorem 9.34 [Cantor-Schröder-Bernstein]