Proof by Induction | Explanation + 3 Examples

In this video, I explain the proof by induction method and show 3 examples of induction proofs! :D
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[@mahfoozali1162]

Trust me guys, he has the best way of presenting the topic!. I've been searching for discrete math vids, and finally found the best one. keep doing what u do✌

[@dylanrobichaud3676]

i’m a junior in college and you covered this material significantly better and more efficiently than my professor. you have a great way of explaining. keep it up man💪

[@saturnrobinson5057]

Thank you!!! Taking a course on linear algebra and one on number theory without taking an intro proof class so we're just kinda vibing over here!

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[@cohenharley1462]

@Kasen Wade I really appreciate your reply. I found the site through google and Im trying it out atm. Looks like it's gonna take a while so I will get back to you later with my results.

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[@kasenwade5386]

@Cohen Harley happy to help :)

[@SomenoobIoI]

Great video, the third example helped me quite a bit!

[@arjay_2002]

is the basis step the base case?

[@zanekovac726]

Thank you, this video made things so clear, the explanation is nice and detailed.

[@rupanbaro5849]

Nice presentation for beginners in

[@k.8597]

I used (7^k = 3 + 4^k) so you end up with 7(7^k)-4(4^k) = 7(3+4^k) - 4(4^k) = 21 + 7(4^k) - 4(4^k) = 21 + 3(4^k) = 3(7+4^k) and since k is a positive integer and the integers are closed under addition and multiplication, 3(7+4^k) = 3z where z is an integer. Bit different but is it still valid?

[@deepstudios3832]

at 13:56, we we are writing what we want to show, why is the 4k - 3 present in addition to plugging k + 1 into k. if we supposed that n = 1, i understand putting 4k + 3, but if we Want to show P(k + 1), wouldnt we just plug in k + 1 wherever n is present (like we did for the right side)?

[@BrainGainzOfficial]

Good question. Yes, you can just replace k with k+1 and simplify (I also did this). Writing 1+5+...+(4k+1) is the same as writing 1+5+...+(4k-3)+(4k+1). I just made the term before 4k+1 more explicit because I think it helps us see how we can show what we want to show (by adding (4k+1) to both sides). If you can do without it then it's still perfectly fine.

[@airylharridzuan6377]

At 24:12 how did you came up with 3 . 7^k+ 4 . 7^k + 4 . 4^k ? Btw thank you so much for your videos! Helped me a lot

[@quelloroberts6310]

im mirin the brain gainz brah

[@glansingColt]

Can you make a vid on Strong induction?

[@gerardsagliocca6292]

I think you should organize your videos by similar topics

[@chrisrodriguez6357]

Can you be my professor?

[@AkhonaAlbertIsaacMali]

Thanks a lot for this. I just want to ask how you got to 23:56. I'm a bit lost at that step. But I understand how you got from there onward.

[@AkhonaAlbertIsaacMali]

Oops. Never mind. I understood just as I typed this comment out. You the man! Awesome videos

[@gerardsagliocca6292]

Should have gotten more board space. It looks crammed.

[@glansingColt]

am paying million dollars for these in college. shame on me

[@hamzarehan1838]

At 18:15 how do you get 2k^2 + 4k + 2 - k -1 from 2k^2-k+(4k+1)? This doesn't make any sense for me.