Discrete Math - 5.2.1 The Well-Ordering Principle and Strong Induction

In this video we introduce the well-ordering principle and look and one proof by strong induction.

Video Chapters:
Introduction 0:00
The Well-Ordering Principle 0:10
Postage Stamp Example Using Induction 2:11
Postage Stamp Example Using Strong Induction 7:01
Up Next 9:35

Textbook: Rosen, Discrete Mathematics and Its Applications, 7e

[mikexrag]

Only resource on the topic of strong induction that's clicked for me. You're gonna go down in some kind of math hall of fame, Prof. Brehm !

[valeriereid]

Dear Professor Brehm, thanks for making these excellent lectures available. I got an excellent mark in my discrete math course this summer. You have boosted my confidence to take Real Analysis this Fall and later Topology. Thanks for taking the time to explain things that often get glossed over in class.

[udbhav]

I wanted to take a moment to express my deepest gratitude for your exceptional way of explaining complex topics. Your passion for teaching truly shines through, and the clarity with which you break down concepts makes learning a joy. This lesson on Strong Induction was particularly enlightening, and I appreciate the effort you put into making it accessible and engaging. Thank you for being such an inspiring and dedicated teacher; your impact is truly invaluable. I'm fortunate to be here.

[bebebewin]

For the stamp problem, to clarify, we are assuming that P(j) holds over the entire range [12, k] where k>=15 because we have proven P(12, 13, 14, 15) in the base step. Then when we are proving that the statement must hold for p(k+1), we can reference the fact that P(j) also holds for all values of [12, k]?

[vidro]

can you expand on why you use p(k-3) ?

[MaskedPolitician]

This video is very helpful thank you. I have a question:
For Strong Induction, your 1H is that P(K-3) is true. Why can't you just say P(K) is true, since you already proved it to be true in the base case?
Then you can still show P(K+1) using the same logic.

[tanhnguyen]

i think we can represent 4, 5 like a number system which has the same function as binary system starting from 12 (4+4+4). I think it's pretty cool at least for me
4+4+5 (13)
4+5+5 (14)
5+5+5 (15)
4+4+4+4 (16)

[karanveersingh]

didn't understand the example so well. Why did u choose such a difficult eXAMPLE?

[rickbman]

Everytime she says "Make Change" I just think of New Jack City 😂

[Karim-lndw]

Very poor explanation of the example with strong induction for the stamps problem. You didn't convince me with strong induction proof