Literally, Professor Brehm saves the day every time. I got stuck wondering where do they get k>10 and came to this video and it is thoroughly explained. Not only that, now I fully understand strong induction.
@SawFinMath2 жыл бұрын
Thank you! Happy I could help!
@faraihnazar6994 Жыл бұрын
I am still not getting it.Please helppppppppppppppppppppp
@_f0xgl0ve Жыл бұрын
Your videos quite literally saved me from failing my discrete mathematics course. Thank you 🙏
@JafarTheJackal2 жыл бұрын
This is the only strong induction video that make complete sense to me. Thank you for your explanation
@eclip1z2 жыл бұрын
i have watched countless videos on this topic. This is by far the best explanation. I finally get it. thank YOU so much. subscribed so quick. I'm going to watch all of these videos. Absolutely amazing. Thank you Professor Brehm. I'm passing my exam.
@VndNvwYvvSvv Жыл бұрын
The prime example seems like circular logic since we assume P(j) for 2 ≤ j ≤ k but this isn't proven, except that's it's asserted for 2.
@vidro36 ай бұрын
i agree. we really just made a hypothesis and then used that to justify the solution.
@jingyiwang5113 Жыл бұрын
I am really grateful for this wonderful explanation! I have been stuck at this point for a really long period of time. And I am very puzzled whenever Professor gives lecture. I finally understand it by watching your tutorial. Thank you so much!
@varshini1745Ай бұрын
you are the best teacher I have ever came across .... such a beautiful explanation with examples that clear the concepts .... love love ma'am
@CrushOfSiel6 ай бұрын
Very nice examples and explannation. I was having trouble figuring out which base cases to include but your explanation around 11:30 really helped me see. I'll probably always make a table with arrows now :).
@wilmercuevas64918 ай бұрын
I didnt understand anything
@voltonator79915 ай бұрын
I’m so cooked bro
@jorji65 ай бұрын
bro me too. if i don't get a 90 in this final i don't pass the class
@RounakrkАй бұрын
@@jorji6did you passed?
@beelzebub3920Ай бұрын
Prolly not honestly. Should've studied earlier
@wavez4224 Жыл бұрын
I’m kinda confused on why we assume p(j) is true for 2
@netanelkaye3014 Жыл бұрын
I'm also confused- do we have to prove the inductive step or not? In this case it seems that we just assume it is true, but we never proved it... (meaning, we never proved that p(j) is true for 2
@wavez4224 Жыл бұрын
@@netanelkaye3014 it’s been while so I do understand it now. Pretty much in weak induction you use the n-1 step to prove the nth step is true. (For example you use 2nd step to prove 3rd is true) In strong induction you use all steps from n-1 to 0 to prove the nth step. (For example you use the n-1, n-2, and n-3, steps to prove the nth step is true) The difference in notation is what makes it kinda confusing. in weak induction we normally use the n-1 to prove the nth step while in strong induction we use the nth and below to prove n+1 step. It’s the exact same concept though it’s just up to notation whether we want to prove the nth step or n+1 step
@netanelkaye3014 Жыл бұрын
@@wavez4224 Right, but in weak induction, we do first prove the n-1 step. we dont just assume the n-1 step is true- we prove it. It seems like in this case, we dont prove all steps from n-1 to 0- rather, we just assume they are true. Am I wrong?
@wavez4224 Жыл бұрын
@@netanelkaye3014 you never prove the n-1 step in weak induction. You only prove the base case and that if you assume n-1 is true then n is true. Same idea here. You prove the case case and then you prove that if all the steps between n and the base case are true then n+1 is true. So we never prove the n-1 step in both weak and strong.
@pibbxtra39696 ай бұрын
This is helpful, but if everything is built on hypothesis after the base case how did we prove anything?
@purpleAiPEy13 күн бұрын
Nice clear video, thanks.
@MuhammadAbdullah-wx1ev6 ай бұрын
will it be all right if I use k>10 instead of k>=10 , I still didn't understand why you used k>=10
@linaaveyaa6 ай бұрын
technically 1 isn't prime so you can't use 2 as your first product of primes because 2 * 1 is not the product of two primes, it's the product of a SINGULAR prime.
@henryqiu2279 ай бұрын
I am sorry I am too silly. I am so confused. the hypotheis only show that p(j) is true for 2
@yrsobeautiful6 ай бұрын
It’s a case we are considering. If k+1 is prime then it is true that k+1 can be written as a product of primes, and no more work is needed.
@noobheadsigma4405 Жыл бұрын
2 being a prime number is not a product of primes. How does the basis step become true?
@noobheadsigma4405 Жыл бұрын
If one of the multiple become prime; then it is enough to be a product of primes?
@ashleighroppolo64387 ай бұрын
2=2•1 A prime number is a product of itself and the prime number one
@mehmetalitoy392910 ай бұрын
Thank you so much, every dumb in internet is explaining the prime question really really bad. This helped too much...
@AR-rg2en2 жыл бұрын
Hello professor, at 2:30, so like 2 can only be written as 2 * 1, but 1 is not considered a prime number. Maybe we have to add "or it is a prime itself" at the end.
@karqoa39682 жыл бұрын
agreed
@tbnman Жыл бұрын
This confused me also. A prime number cannot be represented as a product of primes, because 1 is not prime. I've read numerous texts on this that all assert that any n > 1 can be written as a product of primes. However, when they further explain the statement through proofs, they clarify that n is either prime OR a product of primes. Is this an accepted measure of ambiguity in a field that prides itself on precision?
@VndNvwYvvSvv Жыл бұрын
@@tbnman It can be written as a product of 1 and itself (1). Further pedantry is unnecessary for this special case.
@leonben3921 Жыл бұрын
im assuming that you choose 10 in 10>=k because if it would be 9, then the initial value would not be 8; it would be 7. I think that is how I would have understood why 10
@punditgi2 жыл бұрын
Hurrah for these videos! 😄
@jianqinggao4167 Жыл бұрын
This is so helpful, thank you so much❤
@SawFinMath Жыл бұрын
You're so welcome!
@Burrgundy Жыл бұрын
Thank you!
@xbz245 ай бұрын
thanks
@akikozzm79152 жыл бұрын
in 15:47, I am confused about why P(k-2) is true? we never proved it right?
@SawFinMath2 жыл бұрын
We assume P(k-2) is true, which we can do since we have more than one initial condition. For instance, if P(k) is assumed true, then we know P(k-1) and P(k-2) are true since they are initial conditions.
@AzimMukith11 ай бұрын
I still do not understand why k>=10?
@netanelkaye3014 Жыл бұрын
why cant you just use regular induction to show that you can make $0.08 stamps out of $0.03 and $0.05 stamps? Just use $0.08 as base case and then prove that if you can make $0.0k out of $0.03 and $0.05 then you can make $0.0k+1?