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