Chap. 10 Recurrence Relations
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Chap. 10 Recurrence Relations
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Chap. 10 Recurrence Relations. Discrete Function. A set S is countable if | S | = | N |. Thus, a set S is countable if there is a one-to-one correspondence between N and S. A set S is at most countable if | S | ≤ | N |. Any finite set is at most countable. - PowerPoint PPT Presentation
Transcript of Chap. 10 Recurrence Relations
Chap. 10 Recurrence Relations
Discrete Function• A set S is countable if |S| = |N|. Thus, a set S is countable if
there is a one-to-one correspondence between N and S.• A set S is at most countable if |S| ≤ |N|.
– Any finite set is at most countable.– The set of natural numbers and the set of rational numbers are at most
countable. – The set of real numbers and the set of irrational numbers are not at
most countable. • A discrete function is a function whose domain is at most
countable.– The domain of the factorial function f(n) = n! is NU{0} which is at most
countable. Thus, the factorial function f is a discrete function.
Linear Recurrence Relation
1 1 1 1
Example 10.1
Example 10.4
Example 10.38
Example 10.38
Example 10.38
Example 10.38
Example 10.38
Example 10.39
Example 10.39
Example 10.39
Example 10.40
Example 10.40
Example 10.40
