Induction: Inequality Proofs

[@Tyler-bp4md]

i like the way he teaches. it feels like he's just having a conversation rather than presenting

[@pinklady7184]

I didn't expect him to whistle at the beginning. What a surprise. It means he is *happy.* It must mean something good has happened on that day or week.

[@sahil-xz9en]

@@pinklady7184 psychology student

[@glennredwine289]

@@pinklady7184 I just think he enjoys his job.

[@glennredwine289]

I like his videos but the writing is pretty small, needs to be much larger.

[@glennredwine289]

He has an easy style of teaching. At home with himself, his students and the subject matter. I sub teach HS Algebra & Chemistry in thd Long Beach California and this stuff still stumps me even though I had the class 30+ yrs ago.

[@kasiorap]

you make my college professor look like an idiot, thanks for helping me pass discrete maths bro :,)

[@SuperBluerosa]

this

[@yansteven3437]

my professor makes me look like an idiot. He makes my professor look like an idiot. :)

[@RenanRF77]

Looked at a few books, videos and web pages, but only after watching your video, induction is finally beginning to make sense to me. Thanks and keep up the great work.

[@admin-ts8uv]

This is what teaching should be like, this is professional teaching, I'm taking a discrete math class in college and its making me miserable, these PHD professors are useless!!!!! How come a KZbin tutor is 100000% better than those useless PHD professors at my university, they just over complicate simple things, this is so refreshing. Thank You!

[@mtwchuang]

Thank you Eddie for your teachings, your students are truly blessed

[@marielabusheva7062]

Watching from 2020. I don't understand anything from my online classes in uni. Now I am here and I understand everything. Thank you!!!

[@marcushines4172]

This is so much more intuitive than the way I was taught. Awesome video.

[@Jamony1]

All your induction videos are great :) I didn't do Higher Maths at school so am now doing an equivalent at university this semester so I can pick up maths next semester. We did a single lecture on induction and a few examples and I was really struggling, but I've really started to get it all clear in my head now. Thanks :)

[@iamgeraldable]

You sir deserve more views. We have our Math finals about Pre-Calculus topics and my friend suggested that I go here. I'm not disappointed. Thanks for making induction easier and upload more :D

[@povsurealism1312]

Eddie Woo my uni teachers spent like 2 months explaining this to the entire class and no one got it. But you managed to do it within like 5 seconds of just explaining the most basic logic

[@ChaceRehberg]

Those who teach, in any capacity, need to take notes on this man. He has a unique understanding of communication that engages the audience.

[@theproofessayist8441]

Following your video description wouldn't another way to think why inequality is more flexible than equation simply because it is easier to assume things are unequal than not equal and that equality formally requires two implications to prove (if you think of it as a biconditional) and that inequality only requires one direction. Food for thought and double checking for myself. Great Video. Cheers!

[@bnetjail]

You put this up for free viewing! Amazing. Thank you. I will tell people in my class about this channel.

[@jroberto7143]

This has been the most straightforward explanation! Thank you Mr. Woo, you da real mvp

[@thesecretfiles31]

omg after so watching so many inequality videos and not understanding I finally find yours. Thank you soooo much, you really do know how to explain

[@Mnaim31]

I love the energy he puts in the presentation

[@4ueyescream]

You are the best teacher There are not many like you left - trust me - Im in my final year at school in australia as well and ive never had a teacher quite as clear as you !!!

[@noblessus]

These explanations are excellent. The ones from my textbook are weak compared to the ones used by the professor in this video. Thanks a lot for uploading this video; it was very useful.

[@ifeanyianene6770]

I've been at uni for almost 4 weeks now and this is the first time im understanding this, thanks so much.

[@GamingTherapyZero]

Sir you are a great teacher! coming from one that knows how to decrypt complex ideas to obvious steps you've thought me something I've been struggling on for ages!

[@LoLzWatsUsay]

Thank you so much!! I had trouble for this past month with exactly what you pointed out, the transition between the inequalities. Both the textbook, and my professor chose not to explain why or how it worked Once again thank you so much!! This means a lot to me!!

[@amelianyquist1215]

Thank you so much for this video! Especially the problem with factorials contained in inequalities- I was so confused on how to solve them until I found this video- Keep doing what you're doing please!

[@Placeholder209]

Thanks A LOT for this! You're a great teacher I finally understood

[@DeadDude4]

This explanation is so much better than the one my teacher gave me! Thank you very much for uploading this :)

[@black_winghd1429]

this man just single handedly safed my maths homework and potentially test

[@gabrielortolanioliva2978]

omg he is so amazing this guy is the best teacher i have ever had in my entire life omggg

[@MaatlaLemao]

I have been through all the youtube videos for the past week on this topic and now i finally understand.thank you Eddie

[@aidanlovesit123]

So helpful, my maths lecturer at the university of Liverpool is terrible at explaining this you made it so simple, thanks!

[@Xiorth_YT]

+Aidan Sullivan Small world. I'm a fresher there now doing Computer Science and now I'm here trying to learn it, haha.

[@michaelren7421]

as an nsb student, i can happily say you're the goat

[@michelesilvestri6484]

The GOAT honestly. What a great guy

[@jackhaehl2033]

You saved my discrete math final you're my hero

[@XxProgenitorxX]

Great job by the teacher. Very clear and concise way of proving the inequalities. My textbook is not very clear about these things so this video was a massive help. Thanks for the upload

[@javaz6538]

You are a very awesome person. I can just feel an aura of awesomeness during the videos, and can't help the infectious ecstasy that the math brings you!!

[@otamanlvhs]

Really grateful.It was really hard topic to understand and thanks to you I'm finally starting to understand it.

[@johnnypanrike8505]

Hi Eddie, nice video! I do believe, in the first proof you need to assume that k is nonnegative, rather than just positive to get it to work. Also to support understanding, I'd suggest putting in equivalence arrows () and implication arrows (=>). This might demystify the thing that "in inequalities you can just chop up and move around", with the emphasis on that in inequalities we only need implication, that clarifies :-) Keep up the good work!

[@khivanraina3102]

Eddie Woo's math skills are so great that he woos many

[@sdw4527]

Exceptionally articulate. You made a problem that looked complicated on my midterm study guide easy. Thanks a lot :)

[@happybird2621]

Omg Thank you My teacher could never 👏🏻👏🏻👌🏼

[@tangled55]

I've never seen a Asian with an Australian accent before. He's hot and smart. Great video.

[@tangled55]

You've never heard that you're hot and smart before? lol and you read the comments?! I guess it is your channel. I hope that didn't come off as disrespectful (about the accent/ethnicity thing). Wasn't my intent at all. I learned more from this one video about induction than half a semester on induction. I'll be scanning your videos for help on epsilon-delta proofs too! Thank you so much, Professor/Dr. Woo!

[@tangled55]

***** Haha thank you Mr. Woo! And check your direct youtube messages if you're bored and get the chance! =)

[@michalchik]

***** One teacher to another. You are doing a good job.

[@TheChaster123]

I agree, great job. The book didn't explain it nearly as well as you did.

[@YoshiFujimoto]

Wow, this breaks it down perfectly. Seems so simple and concise. Thanks Eddie!

[@0diepus]

From 7:33 to 8:00, my mind exploded!!!!! It all makes sense now!! Thank you sir!!!!

[@jaredhee4194]

eddie you're actually a king

[@ghotifish1838]

omg this is so much easier to understand what u like about this is how he added an example of the 10 and 5 cause like even when someones head not straight like me, I still finally understand why it worked

[@Loujayn4BetterWorld]

Thanks for this high level explanation. Unfortunately, I haven't worked for a strong base in my last-year Discrete course, which I need today in my Data Structure and Algorithm course and in our CS foundation in general. I can make them as my snacks as they're interesting videos. Thank you so much ^-^

[@harvardford8752]

THANK YOU SO MUCH THIS IS SO HELPFUL I never did understand inequalities quite well, but this is pretty concise

[@patrickmayer9218]

Algebraic trickery! Thanks for making a hard subject understandable!

[@joeybistoocool]

You made everything SO much clearer. Thank you so much

[@tomasasnes4081]

Give this man an award

[@ishitayadav3656]

Thank You so much for this, this was the ONE concept that had driven me up the wall. Thank You.

[@alialden1258]

THAT CLEARS IT UP. I LOVE YOU SIR. KEEP UP THE GOOD WORK!

[@eveodonnell5732]

This helped me so much thank you!! From Ireland 🇨🇮

[@SolidHD1337]

Thank you Mr. Woo, I can now finish the rest of my homework. The inequalities always confused me because I forget you can substitute k+1 with is lowest possible value.

[@FarukqO]

Some teachers are a living proof that no concept is hard

[@hqlife5128]

thank you very much, this is much easier and more logical to follow than the way it is done in my textbook

[@cheekyismymiddlename]

I can't thank you enough! Induction is still the devil to me, but you've helped me grasp the concept of inequalities so much! our teacher just gave us the chapter to do without explaining anything beyond just simple induction THANK YOU.

[@eminemworthy]

you are not only a lifesaver but the best maths teacher alive. i am just wandering, which school do you teach at?

[@GrapJack]

I'm really glad that you showed how to reason the RHS on the factorial example at the end, but for me that seemed harder. If we multiply both sides by 2, then it satisfies our RHS of 2^(k+1) and gives us 2k on the LHS. Certainly, it follows that (2k)! > (k+1)! since 2k > k+1. That's how my brain worked, but thanks for showing the other way!

[@WickedChild95]

Awesome video! The last part with the inequality substitution was really confusing until I saw your video!

[@shirleylove979]

wow wow love your energy for teaching and math. Wish I had you as a teacher in high school.

[@exobytemonolith5339]

The second inequality is actually also true for n=4 4!=4*3*2*1=24, 2^4=16, 24>16

[@faxx1080]

You've just saved me for an upcoming final! Thank you very much for this!

[@listraramrattan2221]

Great vid, but I honestly don't think you look like a teacher, i thought you were a brillant student dressed like a teacher, thanks btw!

[@jessicakraft6854]

oh my goodness, thank you so much, iv been having so much trouble with induction and i cant meet with my professor because her office hours are during my classes. this was so helpful

[@Zippo_1234]

Very good, thank you for explaining how to do these proofs.

[@CarmelLax15]

I wish my professor would explain how everything ties together like you do thank you so much for this video this helped so much

[@seigemain]

literally the best teacher

[@ismailramadani5037]

Thanks a lot, I found it very helpful.

[@jumung2012]

I meant 12:57, but I watched the video again and it made sense, I think I was confusing the direction of the inequality. Thanks for the video!

[@RF-ge8tz]

11:59 how is (k+1)k!=(k+1)! ?

[@alejandrodavidrodriguez7038]

Thank you so much for the clear explanation, you have a gift for teaching and have helped me understand so many topics, not perfect but really good.

[@geotapayan368]

Already 2020 but still helped me a lot. Thank you.

[@Caliemha]

Thanks for the video, this explains it 100 times better than in my textbook :D

[@PauxloE]

In the first example, the induction step needs to work for k = 0 too (not just k > 0) if you anchor at 0. Fortunately it does, though 6·k > 2·k weakens to 6·k ≥ 2·k.

[@GeorgWilde]

7:30 There is a mistake, *k* should range on non-negative integers {0,1,2,...} - it has to include the base case *k* =0. This also means that 6k > 2k is wrong (try to plug in zero), it shuld be 6k >= 2k.

[@sunsetsimp425]

But if it's given k is a positive integer, it's obvious we start with 1. So turns out 6×1>2×1. And then it goes on for 2, 3, etc.

[@instaminox]

@11:54 seconds how did you assume that the LHS was set ? please you may clearify that for future student. Thank you in advance.

[@irosnake]

OMG thank you so much! Your teaching is so clear and simple to understand :DD i was wondering if you could do videos on discrete mathematics modules.. such as Relations and Functions.

[@anon221]

Been stuck on this for a while, thank you so much for the good explanation!

[@dlu0813]

The first example also comes directly from Bernoulli's Inequality. But thank you Mr. Woo for teaching these examples! 😄

[@patricknazar]

Dude this is so good. THANK YOU

[@sorenfox]

Thanks! My Math-Specialist teacher apparently decided we didn't need to know this, despite it being in our course outline...

[@thies2us]

(k + 1) k! > (k + 1) 2^k (k + 1) > (k + 1) 2^k what happened to k! on this line at 12:30

[@lunethia2]

thies2us (k+1)! = (k+1)(k)! = (k+1)(k)(k-1)! and so on

[@zamgill]

Thanks so much for a great explanation! Finally understand this!

[@jonasbertels861]

Thank you so much, I had so much trouble with that one step (going to show that if 6k+3 is less then 3^k, so is 2k+3.)

[@aaron___6014]

Thanks for the video, I wish my professor would simplify things as you do. I've broken these induction problems into the same steps you've mentioned, yet my professor has never mentioned steps for any problem.

[@mib141345]

You just cleared....so many of my doubts! Thanks!

[@Salamanca-joro]

best explanation for this topic

[@samuelhyeman7851]

Why is the quality of your video so good?

[@MohammadYaseen-oz6lo]

That's what he does different his quality where the last point in the prove where everyother video fails to explain that bruh "This is a bit hard to get around ,Yeah this is not a big deal for me but I know it is for you it was for me when I started out ,I FEEL YOU " just that explanation makes the change ( Those little but really valuable tiny details)

[@TrueHistoryAustralia]

Thankyou Mr. Woo! Never thought someone could be so helpful from 100s of kms away. Great stuff. Personally I prefer this method to the way I was taught because of the way that the logic flows. Thanks heaps!

[@moutonguerrier]

Eddie Woo @13:12 how does (k+1)*2^k become 2*2^k... basically how does (k+1) become 2?

[@moutonguerrier]

Since k > 4 at the basis step, I understand the inequality stands if you decide k+1 is equal to 2... but do you decide this solely based on your assumption (goal)... because for the induction steps, if we were to compute them, then k+1 would start at 6... anyway I think I just answered myself with : "the inequality stands if you decide k+1 is equal to 2" and "you choose =2 because that's where you want to be heading for your proof".

[@efrainrodriguez8426]

You are my hero! Thank you Mr. Woo!

[@flarros]

Thank you soooooo much! The way my teacher explained this left me completely lost.

[@jamesbond-ch6zh]

THANK YOU EDDIE CLUTCH!

[@kurchak]

@12:38 You say "If you are multiplying by k+1 then you are multiplying by AT LEAST 5. However, k > 4 which means k itself is at least 5. Therefore: k + 1 is AT LEAST 6. Is this correct?

[@kurchak]

Although I do realize that it doesn't change the point that k+1 > 2 lol. Still works. But still haha.

[@SuperIsaac1000]

What you say is true, but it is also irrelevant. This is because k+1 only has to be bigger than 2.

[@kurchak]

Thank you. It is relevant to my understanding. Making sure I didn't miss something. True none the less.

[@fredrickkabwe4742]

k must be greater than 4 ,meaning k can be 5 orgreater

[@pc_gamer76]

7:37 If n>10, it does not imply that n>5, does it? Because it n is strictly greater than 10, then it can't be a number less than 10 but a number greater than 5 can be less than 10.

[@arm4life87]

n is greater than 10, so there for n is greater than all numbers 1 through 10, 5 being one of those numbers.

[@kurchak]

You are throwing an extra variable into this, that's the problem. He said "If n>10, then n>5" You said "if n>10" which is correct, but then you start to talk about some other unknown number (lets say m) that is greater than 5 but less than 10. That is where you are messing up. You are comparing n to some number m which you claim is between 5 and 10. But that isn't what he was talking about. He is saying "If n>10, then n>5". Does this make sense?

[@harderhscmaths]

Nicely done Eddie!

[@thepar4n0id]

12:28 I don't understand why multiplying my something bigger than 2 (in this case k+1 which is at minimum 5 allows us to substitute) Let's say 10>2(3) is true but 10>5(3) is not So I don't understand your logic. Any help appreciated

[@davidrock3936]

***** Hi Eddie, this is a great example of a method for finding these proofs. The part that I get hung up in is with the algebraic manipulation of inequalities. Would you know of any good online resources that provides an extensive review of those principles?

[@ifeanyianene6770]

Do you have any videos on any of these Counting Principles, double counting, subsets and permutations, partitions, generating functions, derangements and principles of inclusion & exclusion?

[@mohammedhisham107]

Very helpfull, Thanks a lot Eddie !

[@jdklenke]

Absolute life saver, thank you so much.