Handouts on Mathematical Induction and the Well Ordering Principle for M 325K Spring 2024

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Click on the desired handout name.

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• The Well-Ordering Principle for the Integers

  • Attached is: Proof that 1+2+...+n = (n)(n+1)/2 Using the Well-Ordering Principle of Z

• An Example Proof using the Well-Ordering Principle
• A Second Example Proof using the Well-Ordering Principle
• Two Proofs of the Same Statement -- One with Strong Mathematical Induction and One using the Well-Ordering Principle
• Proof of the Quotient-Remainder Theorem
• The Principle of Strong Mathematical Induction

  • Attached is: An Example Proof by Strong Mathematical Induction

• Two Proofs of the Same Statement -- One with Strong Mathematical Induction and One using the Well-Ordering Principle
• The Principle of Mathematical Induction

• Attached is: A Simple Induction Proof About a Sequence
• Attached is: A Third Example of a Proof using the method of Mathematical Induction (on pages 7-8 of the handout above: The Principle of Mathematical Induction )
• Attached is: The Proof of Proposition 5.3.2 in Dr. Shirley's Format

  • Note: You will need this result for use in working HW #6, namely for Problem #19 of Section 5.3

• Attached is: Example Proof by Mathematical Induction -- Problem #11 of Section 5.2 Solution

• Example Proof Segments of Proofs by (Regular) Mathematical Induction
• The Basis Step Worksheet
• The Basis Step Worksheet Solutions

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