§2.4 Cardinality(基数） (1) Definition 1 (page 158) The sets A and B have the same cardinality if and only if there is a one-to-one correspondence from A to B. (2) A set that is either finite or has the same cardinality as the set of positive integers is called countable. A set that is not countable is called uncountable.
Examples Example 18: Show that the set of odd positive integers is a countable set.
Examples Example 19: Show that the set of all integers is countable.
Examples Example 20: Show that the set of positive rational numbers is countable.
Examples The set of rational numbers is countable?
Theorem: If the set Ai (i=1,2,….)is countable, then A= ∪i=1∞ Ai Is a countable set.
Examples Example 21: Show that the set of real numbers is an uncountable set.
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