This was super helpful! I didn't understand how to decide how many base cases to do before watching this.
@brianeibert1647
6 жыл бұрын
This is the best explanation of Strong Induction I have found. Thank you!
@parkerbrandt1287
3 жыл бұрын
they say this is a strong example but he just pulls that formula at 3:40 outta nowhere, i did the math and idk where the 40 and 80 is coming from wtfffff
@runekid2
7 жыл бұрын
who else is here cuz of the discrete final exam
@cziegl3r
7 жыл бұрын
Speaker of Memes porn hub got boring.. and my proofs finals coming up.
@rook37
5 жыл бұрын
i just came here to cram for my final and honestly im feeling so attacked right now
@Anand-wi4yb
5 жыл бұрын
I am here cuz of my First quiz in Algorithm Design and Analysis Course!
@lck843
4 жыл бұрын
I am here cuz can't solve a problem
@m.xnt_
3 жыл бұрын
*algebra I final
@runekid2
7 жыл бұрын
who else is here cuz of the discrete mid term
@bla7bla7bla74
7 жыл бұрын
lol same
@JJ-ey3dg
7 жыл бұрын
ayy lmao
@jondabomb2184
6 жыл бұрын
1 year later ... me too lol
@richardnguyen5949
6 жыл бұрын
Me too, 1 year later... FML
@FatmaYousuf
6 жыл бұрын
same
@garbagecuber6502
6 жыл бұрын
Scroll back up and pay attention! Thank me later
@yodai3393
4 жыл бұрын
thank you
@AbdelghaniAzzi
4 жыл бұрын
This is so far in my research the best discourse about strong induction. Thank you. Still I don't see the usefulness of assuming that g_i =i! for all 3=
@jonpape
3 жыл бұрын
That was wonderful. So clear and to the point.
@everythingsoftware8539
7 жыл бұрын
In the last example, can I write (k+1) as (K-4)+5 and continue the proof that way? Also in that case, I would make sure that my base cases include 8, 9, 10, 11 and 12. Is it possible?
@kazenohito7641
8 жыл бұрын
Very helpful to a cs student taking fundamental structures and learning the induction method. But please write out your methods. It helps alot looking at your example I kept up with you until you started your expansions then you lost me completely.
@hathawayamato
8 жыл бұрын
+Kaze No Hito FYI for the first example he used binomial expansion, if knowing that is of any help.
@Uncertaintycat
7 жыл бұрын
it should say "by the binomial expansion" in a proof if it does that.
@rook37
5 жыл бұрын
@@hathawayamato OH man thank you that makes so much more sense. this was prime 'rest of the fucking owl' material until i saw your comment.
@Matthew-McCallister
10 ай бұрын
I have a higher math midterm on Tuesday. You’re a lifesaver!
@BondedSeven
6 жыл бұрын
I don't understand how you knew [(k+1)k(k-1))](k-2)! is equal to (k+1)! can you explain this? I would never be able to think that this is equal to (k+1)! at the top of my head.
@cjf6568
6 жыл бұрын
[(k+1)k(k-1)](k-2)! = (k+1)k(k-1)(k-2)(k-3)...1. So, all natural numbers less than or equal to k+1 multiplied together, so equal to (k+1)!
@kevinf1920
6 жыл бұрын
(K+1)! is what we were looking for, so it sorta pops up in the mind as the goal. (K+1)! = (k+1)(k+0)(k-1)(k-2)! (Although the 0 doesn't need to be written).
@aalokakanhere4673
2 жыл бұрын
In the first example, one does not need strong induction. It can be done with the first principle too.
@aimee2984
8 жыл бұрын
This was so helpful as an extension to my proofs class, thank you!
@jerryzamora257
7 жыл бұрын
Great video! Thank you. I just have one question: on the first example, how did you get the '2' in [(k-1) + 2]^5?
@joshuastander2697
7 жыл бұрын
Jerry Zamora (k + 1) = (k - 1 + 2)
@fashionvella730
3 жыл бұрын
@@joshuastander2697 i was also confusedan you helped me
@munahassan9860
2 жыл бұрын
Just so I'm understanding correctly at 6:05 , if K-1
@McJerkface
2 жыл бұрын
Yes, since it means (less than) OR (equal to), it only needs to meet one of these conditions for it to be true.
@owenhustles2056
Жыл бұрын
Thank you Mr. Barrus from a UCSC CS major!
@cristianandrei811
3 жыл бұрын
Thank you so much I know you have 69 comments and that number is perfect but I really want to tell you thank you because up until this video I had no idea wth I was doing with strong induction. Thank you Dr. Barrus
@samuelross8036
8 жыл бұрын
I would like to know, if possible, where the example 2 was taken. Is is part of a book ? Which one ? Thank you
@seifabdelkefi1429
3 жыл бұрын
I whish I could press the like button twice..
@jaemichael8584
4 жыл бұрын
11:10 How does that go from line two to line three? I have a polynomial in my line three.
@logancope21
4 жыл бұрын
You may not need this anymore since you asked 2 months ago, but just in case, here's how: Expanding the three terms individually: (k + 1)^3 = k^3 + 3k^2 + 3k + 1 -(3k + 1)^2 = -3k^2 - 6k -3 2(k + 1) = 2k + 2 So: k^3 + 3k^2 + 3k + 1 -3k^2 - 6k -3 + 2k + 2 Combine like terms: = (k^3 - k) then just add the (k - 2)! back in for the answer of (k^3 - k)(k - 2)!
@zertbrown4642
2 жыл бұрын
thx for showing the pattern for example 3
@fashionvella730
3 жыл бұрын
very lovely explained
@mounirzouhari6453
Жыл бұрын
Very good explanation
@jesserosenthal9606
7 жыл бұрын
I'm sorry but at video section 1:12 what do mean 10 does go into zero? That doesn't make sense.
@SecureOpsWizard
7 жыл бұрын
meaning 0 can be divided by 10. (0/10).
@jesserosenthal9606
7 жыл бұрын
Ok now that is the correct way to express that 0 divides by 10 not goes into 10. It confuses people.
@AhmadRadwanalarfdah
7 жыл бұрын
You can actually say 10 goes into 0, 0 times.
@IoannesPaulusMagnus
7 жыл бұрын
10 divides 0 if and only if there exists an integer q such that 0 = q * 10.
@pranavyeole102
2 жыл бұрын
great video thank you very much
@joshmckinney6034
2 жыл бұрын
Amazing explanation
@zhuoxuanli6566
4 жыл бұрын
this vido is very helpful at all !!
@srp3151
Жыл бұрын
Thank you Michael. Great explanation!
@dhruvmittal4316
4 жыл бұрын
We love you Mr.Barrus !!!
@vannesdharmawan9551
3 жыл бұрын
Sorry but isnt 80 in the 80(k-1)² supposed to be 120?
@farzadsaeidi2120
5 жыл бұрын
Are Strong induction and Structural induction identical?
@vinayak186f3
4 жыл бұрын
Best explanation ! 🔥🔥🔥 Thank you ❤️
@johnfei434
4 жыл бұрын
You are awesome. Thank you!
@morganoh3332
7 жыл бұрын
Why did k-2 have to be greater than the base case 10?
@jiawei8244
4 жыл бұрын
Very helpful! Thank you!
@nafeeahnaf6296
9 ай бұрын
man wtf is this topic watched the whole thing and understood absolutely nothing
@srikanthemani9528
3 жыл бұрын
now i can solve strong induction problems.
@avichein2702
6 жыл бұрын
Good stuff!
@vgmastercleveland
5 жыл бұрын
This guy sounds Canadian. Are you Canadian?
@HassanNasruMohdKamil
8 жыл бұрын
On example 2, shouldn't i be between 4 and k instead of 1 and k?
@michaelbarrus9935
8 жыл бұрын
No, in your induction hypothesis you need to allow the possibility that i equals 1 or 2 or 3 in order to have your proof hold for n=4, n=5, and n=6. In general, you'll typically want to keep your attention on the theorem statement (that g_n = n! for all natural numbers...meaning for all integers n from 1 on) and use that first possible value (1, here) in saying what i should be allowed to start from. (Be careful not to be distracted by the fact that the recurrence applies when n is at least 4--we're not proving the recurrence (we're just using it), so the important thing is to focus on the statement you're trying to prove.)
@HassanNasruMohdKamil
8 жыл бұрын
Thank you! Your explanation made much sense. I was trying to form a pattern for the inequality of i's from the examples so I got slightly confused. I understand that strong induction revolves around the idea of the numbers preceding k to be true but it's hard to establish the grounds for the method sometimes. In time I'll get the hang of it
@safeamiiir
7 жыл бұрын
It was such a Great teaching I've ever seen !
@bokpokbok3129
6 жыл бұрын
Thank you!
@mrbrokenenglish2700
5 жыл бұрын
wooow be my teacher
@darlzchriz1320
8 жыл бұрын
nice
@abidhossain8074
3 жыл бұрын
thank you a lot
@williamboafo8514
3 жыл бұрын
Uconn represent!
@Jessica-nk4wo
8 жыл бұрын
Thank you =)
@m.xnt_
3 жыл бұрын
to anyone reading this, please help me with a strong induction proof problem:( i'm stuck
@aniakrzeminska6776
7 жыл бұрын
who else is here for IB discrete math exam this monday
@MaddoSheffu
4 жыл бұрын
Test Neprošel
@ozangurcuoglu789
10 ай бұрын
Adamsn ab 12:06
@shreeganesh441
6 жыл бұрын
who else is here to just learn strong induction for high school olympiads?
@mattbekhterev1249
4 жыл бұрын
Shree Ganesh kindergarten Olympiad’s actually bud
@elchinmammadov624
6 жыл бұрын
Would be great video if you didnt keep making that weird sounds out of your mouth every 5 seconds.
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