11: Recurrence and induction
- Page ID
- 83456
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- 11.1: Sequences
- Counting Set: the set N<m={n∈N|n<m}={0,1,…,m−1}
- 11.2: Recurrence Relations
- Recursively-defined sequence: a sequence {ak} from a set A, where a0,a1,…,aK−1 are defined explicitly, and for k≥K, the term ak is defined in terms of some (or all) of the previous terms in the sequence a0,a1,…,ak−1
- 11.3: Solving through Iteration
- Given a recursively defined sequence {ak}, we can “unravel” the recursive definition to determine an explicit formula for the general term ak which involves only the index k.
- 11.4: Inductive definitions
- We can use the idea of recursive definitions in a more general manner.