CS336f1013 - Lecture 13 CS336 Definition The sets A and B...

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10/17/10 1 Lecture 13 CS336 Cardinality Definition The sets A and B have the same cardinality if and only if there is a one-to-one correspondence between A and B. Definition The initial definition of finiteness says a set is finite if we can “count” its elements. Counting means establishing a one-to-one correspondence with a set of consecutive integers beginning with 1 up to an integer n. The fact that is one-to-one and onto ensures that each element of A is counted (onto-ness) and that no element is counted more than once (one-to-one-ness). Example: What is the cardinality of {0,1}? Definition A set is infinite if it is not finite. Definition 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. Example 1: Show that the set of even positive integers is countable. Example 1 Show that the set of even positive integers is countable.
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10/17/10 2 Example 1
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