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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:
      • \(\sum_{k=1}^{n} a_{k}=a_{1}+a_{2}+\cdots+a_{n}\).

    This page titled 8.6: Summary is shared under a CC BY-NC-SA 2.0 license and was authored, remixed, and/or curated by Dave Witte Morris & Joy Morris.

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