Discrete Math II - 5.1.1 Proof by Mathematical Induction

Though we studied proof by induction in Discrete Math I, I will take you through the topic as though you haven't learned it in the past. The premise is that we prove the statement or conjecture is true for the least element in the set, then show that if the statement is true for the kth element, it is true for the (k+1)th element. We will go through just one example and show the steps used for a proper proof. The follow-up video for section 5.1 is all practice proofs.
Video Chapters:
Intro 0:00
What is Mathematical Induction 0:07
Well-Ordering Principle 2:02
Back to Induction 4:19
Guided Practice Proof 5:16
Up Next 12:54
This playlist uses Discrete Mathematics and Its Applications, Rosen 8e
Power Point slide decks to accompany the videos can be found here:
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The entire playlist can be found here:
• Discrete Math II/Combi...

[@user-hd7ki7xq8u]

You should take the sum of I.H (k^2) and substitute that in for 1 + 3 + 5 + … (2k - 1) since we are assuming they equal each other. So you can now do, k^2 + 2k + 1 = (k + 1)^2.

[@karqoa3968]

thank you very very much for these videos

[@UserXpro77]

Thanks for the course, but this should be seen according to the roden of the youtube playlist or according to the number of the videos "5.1.1, 5.1.2......"?

[@sedibe]

you r the best

[@alifnm3607]

[@caitbenn365]

Great video. Why did you add 2k+1 to both sides?

[@SawFinMath]

That is the definition of an odd integer

[@feltonkaonga]

❤👍

[@karitrik3606]

very complex video