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
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!
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...
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?
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.
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.
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!
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...
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
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.
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.
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
What an absolute timeless, gem of a video - 4 years later and it's still helping. Much love to you
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!
Wonderful explanation. I appreciate how you explain each step.
Thank You so much for the STRONG explanation. You sir are a saint.
best explanation ive ever seen yet!
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...
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?
OMG I finally UNDERSTAND!!!!!!!!
Very nice question.
Beautiful explanation. Thank you!
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.
Excelent content
Wow, you explain it so clearly in the video. I wish you were my prof
Nice, loved it
Really good explanation.
great sir. super clear now. thanks you are a genius.
we spent a week on this and ive spend 20 minutes watching your videos and learned more im so done
Thank you for such clear explaination!
Excellent explanation!! Thank you!
Thankyou so much. This helps a lot
Thankyou 🌻
Loved the vid, not sure what you're writing or if you're writing backwards but still amazing vid
The vid has probably been mirrored, notice how he is writing with his left hand.
sir, you are amazing.!!! thank you.
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.
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!
@@gabrielfernandes8401 Now I see the tru reason behind strong induction, thank you!
great explanation! thank you! i wish my prof explained it like this ngl
explanation aside is he writing backwards on the board?? or what is happening
Mirrored
amzing :)))
Discrete structures Exam 3 in 14 hours.
Failed the last 2 exams.
God let me hold the power of mathematical knowledge
Thank you this helped a lot
HOW ARE U WRITING?!?!? HOW R U BENEATH THE SCREEN
looks kinda op they gotta nerf this
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...
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
anyone notice how most of the professors on yt r left handed
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.
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.