Presentation 1 O'Neill
-
Upload
shannononeill422 -
Category
Education
-
view
122 -
download
0
Transcript of Presentation 1 O'Neill
![Page 1: Presentation 1 O'Neill](https://reader035.fdocuments.net/reader035/viewer/2022081504/55c67b9ebb61eb6e578b45c7/html5/thumbnails/1.jpg)
SHANNON O’NEILLPORTFOLIO 1
SEPTEMBER 25 T H 2014
Proofs Using Mathematical
Induction
![Page 2: Presentation 1 O'Neill](https://reader035.fdocuments.net/reader035/viewer/2022081504/55c67b9ebb61eb6e578b45c7/html5/thumbnails/2.jpg)
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
![Page 3: Presentation 1 O'Neill](https://reader035.fdocuments.net/reader035/viewer/2022081504/55c67b9ebb61eb6e578b45c7/html5/thumbnails/3.jpg)
The Basic Step
Prove P(n) works for the least elementSkipped Terms
Need to use Strong InductionsCarry out Basic Step for all skipped terms
![Page 4: Presentation 1 O'Neill](https://reader035.fdocuments.net/reader035/viewer/2022081504/55c67b9ebb61eb6e578b45c7/html5/thumbnails/4.jpg)
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
![Page 5: Presentation 1 O'Neill](https://reader035.fdocuments.net/reader035/viewer/2022081504/55c67b9ebb61eb6e578b45c7/html5/thumbnails/5.jpg)
USE INDUCTION TO SHOW THAT
Example Problem
![Page 6: Presentation 1 O'Neill](https://reader035.fdocuments.net/reader035/viewer/2022081504/55c67b9ebb61eb6e578b45c7/html5/thumbnails/6.jpg)
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)
![Page 7: Presentation 1 O'Neill](https://reader035.fdocuments.net/reader035/viewer/2022081504/55c67b9ebb61eb6e578b45c7/html5/thumbnails/7.jpg)
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