presentation 1 o'neill

SHANNON O’NEILLPORTFOLIO 1

SEPTEMBER 25 T H 2014

Proofs Using Mathematical

Induction

The Basics

What’s a Natural

Number? Positive integers Counting

numbers Starts at 1 (WOP) Increases in

increments of 1

Concepts in Induction

Start at the beginning

Getting to the next number

Getting to infinity

The Basic Step

Prove P(n) works for the least elementSkipped Terms

Need to use Strong InductionsCarry out Basic Step for all skipped terms

The Inductive Step

Start by assuming P(n) is true“Break-down” P(n+1) into easier partsUse your induction assumptionShow P(n+1) is true

USE INDUCTION TO SHOW THAT

Example Problem

Review

Want to watch more great videos about induction?

See what Patrick has to say.

Basic Step InductionProve your

statement is valid at its starting point

(WOP)

Assume P(n) to show P(n+1)

All images used have been modified from Microsoft ClipArt.JMT, Patrick. "PatrickJMT." PatrickJMT. Think Well, n.d. Web. 25 Sept. 2014. <http://patrickjmt.com/>.Krantz, "Elements of Advanced Mathematics" (3rd ed.)

Sources