CMPSC 40 Lecture Notes - Lecture 11: Aleph Number, Bijection, Arithmetic Progression
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No searching algorithms will be on the midterm. Sequence = a mapping from the set of natural numbers to a set of objects. Four ways of writing the sum of the terms. These are all equal to: is called the index of summation. To write the product of the terms : Given a finite sequence , the associated finite series is the summation of the terms. Given an infinite sequence , the associated infinite series is the summation of the terms. The sequence of partial sums associated with a series is. To compute the sum of the terms of a geometric progression: Adding together the terms of a sequence gives a series. The sequence of partial sums associated with the geometric series is or. 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.