CMPSC 40 Lecture Notes - Lecture 19: Aleph Number, Search Algorithm, Linear Search
Document Summary
Definition: a set that is either finite or has the same cardinality as the set of positive integers. Definition: the cardinality of a set is equal to the cardinality of a set , denoted if and only if there is a one-to-one correspondence (i. e. a bijection) from to. If there is a one-to-one function (i. e. an injection) from to , the cardinality of is less than or the sae as the cardinality of , written. When and and have different cardinality, we say that the cardinality of is less than the cardinality of and write ( ) is called countnable. A set that is not countable is uncountable. The set of real numbers is an uncounrable set. When an infinite set is countable (countably infinite) its cardinality is. We write and say that has cardinality "aleph null" sequence indexed by the positive integers: has the same cardinality as if there is a one-to-one correspondence from to.
