If anyone is watching this video, then note my words... He is the best teacher in case of teaching strong induction.... I haven't experienced his other videos but he teaches strong induction v well
@marienbad2
3 жыл бұрын
Such an amazing explanation. I am not at this level of math but I love the way the ideas here are presented, and the enthusiasm of the presenter. Good luck with the channel, you deserve a lot more subs!
@justinburzachiello2318
3 жыл бұрын
Wonderful explanation. I appreciate how you explain each step.
@Youngballer739
Жыл бұрын
best explanation I've seen so far, I was wondering about the very last part how do we know that the product of products of primes is a prime or product of primes?
@odinsrensen7460
3 жыл бұрын
This was the presentation of this example of strong induction (prime number or product of) that finally made me understand the logic behind it. Thanks. [edit] aaand now I've lost it again...
@nrgking1667
Жыл бұрын
OMG I finally UNDERSTAND!!!!!!!!
@reddd6916
2 жыл бұрын
best explanation ive ever seen yet!
@jonayedmohiuddin538
Жыл бұрын
I was studying strong induction from a book. And then I got confused and got into youtube and youtube just recommended me this. Just how the hell youtube knows I was reading strong induction :O.
@simpill81
3 жыл бұрын
How did you just assume that k+1 is prime without showing that it is/could be??? Because you have only assumed that P(2).....P(K) is either prime or a product of primes. The second part dealing with composites is a great explanation though.
@gabrielfernandes8401
2 жыл бұрын
Hi! I may be 6 months late, but I'll try to answer that. (K+1) is an integer, so it is EITHER prime OR it's composite. These are the two possible cases and this proof addresses both. In Case 1 (where k+1 is prime) it already satisfies what we're trying to prove. In Case 2 (where k+1 is composite) the presenter shows how it still satisfies what we're trying to prove. Since it works with all cases (there are only 2 cases), the proof is sound!
@DaiMoscv
2 жыл бұрын
@@gabrielfernandes8401 Now I see the tru reason behind strong induction, thank you!
@kaelmercury2966
2 жыл бұрын
Very nice question.
@titan1235813
2 жыл бұрын
Beautiful explanation. Thank you!
@vinnypharmacist
2 жыл бұрын
Wow, you explain it so clearly in the video. I wish you were my prof
@RobertturtleMcNugget
4 ай бұрын
Loved the vid, not sure what you're writing or if you're writing backwards but still amazing vid
@pseudolullus
4 ай бұрын
The vid has probably been mirrored, notice how he is writing with his left hand.
@roger_ando7895
Жыл бұрын
Nice, loved it
@peachyx2187
11 ай бұрын
explanation aside is he writing backwards on the board?? or what is happening
@amogusamongus
9 ай бұрын
Mirrored
@luisantonio7191
Жыл бұрын
Excelent content
@ibtisamali2329
Жыл бұрын
Thank you for such clear explaination!
@Rudra-go6us
3 жыл бұрын
great sir. super clear now. thanks you are a genius.
@firdausspusma8476
3 жыл бұрын
Thankyou so much. This helps a lot
@cgfam5256
2 жыл бұрын
Excellent explanation!! Thank you!
@VC-dm7jp
3 жыл бұрын
Really good explanation.
@mehmetnadi8930
Жыл бұрын
great explanation! thank you! i wish my prof explained it like this ngl
@Kitt262
Жыл бұрын
Can someone explain how this isn't circular reasoning? you're assuming something true to prove that that the same thing is true? I know I'm missing something but I'm not sure what...
@PlaXer
Жыл бұрын
ik it seems crazy lol, but it actually makes complete sense on a logical point of view. It just seems a bit "overpowered" becaue you can assume everything before is true, but if (k+1) wasn't you wouldn't even be able to get to that value
@conformitycontrol7702
2 жыл бұрын
Thank you this helped a lot
@captainfoodman
3 жыл бұрын
sir, you are amazing.!!! thank you.
@littlethings8067
Жыл бұрын
Thankyou 🌻
@dr1lltrckz147
2 жыл бұрын
Discrete structures Exam 3 in 14 hours. Failed the last 2 exams. God let me hold the power of mathematical knowledge
@yongkangchia1993
2 жыл бұрын
amzing :)))
@PlaXer
Жыл бұрын
looks kinda op they gotta nerf this
@juvia1773
6 ай бұрын
HOW ARE U WRITING?!?!? HOW R U BENEATH THE SCREEN
@iuseyoutubealot
Жыл бұрын
anyone notice how most of the professors on yt r left handed
@charlesreed8420
Жыл бұрын
How can this be considered valid? The logic is circular... Youre basing the final statement being true on an unproven assumption, and proving that the assumption is true based on the final statement's validity, which is based on the unproven assumption.
@alexsunderhaft722
Жыл бұрын
Probably the easiest way to think about it is that the assumption is not used to prove/derive something else, but rather to check the only case in which a counterexample could appear. To explain further, the assumption does not have to be proven, but rather the implication that it is part of. For implication, if the premise is false, then implication is automatically true. So here, if [for all k, P(1)...P(k)] is false, then [for all k, P(1)...P(k) -> P(k+1)] is true. And of course in the video the premise is assumed true and it is proven that P(k+1) is true, so the implication holds whether the assumption is true or false. If the implication is true, then the assumption will ALWAYS be true when climbing the ladder. The base is true, so right away the assumption is true for k=1, and by proven implication you know the next is true, so the assumption is also true for k=2, and you can go on and on.
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