Discrete Mathematics - Vol 1 | 12. Induction by Abraham | Learn Smarter
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Knowledge
12. Induction

Proof by induction is a vital method for proving universally quantified statements in mathematics. The chapter introduced both regular and strong induction, demonstrating their equivalence and applicability through various proofs. Moreover, it highlighted common mistakes made during induction proof approaches, emphasizing the importance of establishing base cases and proper inductive steps.

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Sections

  • 12.1

    Discrete Mathematics

    This section introduces proof by induction, a fundamental technique in discrete mathematics used to prove universally quantified statements.

    Learning Practice

  • 12.2

    Induction

    This section introduces proof by induction, a fundamental mechanism in discrete mathematics, specifically focusing on its forms: regular induction and strong induction.

    Learning Practice

  • 12.2.1

    Introduction To Proof By Induction

    This section introduces proof by induction, a fundamental method for demonstrating universally quantified statements in mathematics.

    Learning Practice

  • 12.2.2

    Argument Form Of Induction Proof

    This section introduces the argument form of induction proof, detailing its premises and the validity of the mechanism through visual analogies and examples.

    Learning Practice

  • 12.2.3

    Validity Of Proof By Induction

    This section introduces the validity of proof by induction, discussing its mechanisms, the concepts of regular and strong induction, and demonstrating their equivalence.

    Learning Practice

  • 12.2.4

    Base Case And Inductive Step

    This section introduces proof by induction, outlining the base case and inductive step, crucial for proving universally quantified statements.

    Learning Practice

  • 12.2.5

    Common Mistakes In Proof By Induction

    This section explores common mistakes made in proof by induction, emphasizing the importance of both base cases and inductive steps.

    Learning Practice

  • 12.2.6

    Strong Induction

    This section introduces proof by induction, explaining its two forms: regular induction and strong induction, as key mechanisms for proving universally quantified statements.

    Learning Practice

  • 12.2.7

    Fundamental Theorem Of Arithmetic

    The Fundamental Theorem of Arithmetic states that any positive integer greater than one can be expressed uniquely as a product of prime numbers.

    Learning Practice

  • 12.2.8

    Example Of Strong Induction

    This section introduces proof by induction, focusing on its two forms: regular induction and strong induction, with practical examples to illustrate each method.

    Learning Practice

  • 12.2.9

    Comparison Of Regular And Strong Induction

    This section discusses the differences between regular induction and strong induction, two mechanisms used for proving universally quantified statements in mathematics.

    Learning Practice

  • 12.2.10

    Equivalence Of Regular And Strong Induction

    This section introduces proof by induction, detailing regular and strong induction and demonstrating their equivalence.

    Learning Practice

References

ch12.pdf

Class Notes

Memorization

What we have learnt

  • Proof by induction is a met...
  • Regular and strong inductio...
  • The inductive step and base...

Final Test

Revision Tests