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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.

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Chap. 10 Recurrence Relations

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  1. Chap. 10 Recurrence Relations

  2. 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.

  3. Linear Recurrence Relation 1 1 1 1

  4. Example 10.1

  5. Example 10.4

  6. Example 10.38

  7. Example 10.38

  8. Example 10.38

  9. Example 10.38

  10. Example 10.38

  11. Example 10.39

  12. Example 10.39

  13. Example 10.39

  14. Example 10.40

  15. Example 10.40

  16. Example 10.40

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