8.6: Summary
- Page ID
- 23932
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- Important definitions:
- proof by induction
- base case, induction step
- induction hypothesis
- relatively prime
- Whenever you need to prove a statement with an \(n\) in it, you should consider using induction.
- Sequences of numbers are sometimes defined “recursively,” which means that the value of a term may depend on previous terms.
- There are several alternate forms of induction, including strong induction, generalized induction, and strong induction with multiple base cases.
- \(\mathbb{N}\) is well-ordered.
- If \(a\) and \(b\) are relatively prime, then \(ma + nb = 1\), for some \(m, n \in \mathbb{Z}\).
- Notation:
- \(\sum_{k=1}^{n} a_{k}=a_{1}+a_{2}+\cdots+a_{n}\).