Induction: Inequality Proofs
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- čas přidán 6. 02. 2013
- Proving inequalities with induction requires a good grasp of the 'flexible' nature of inequalities when compared to equations. Make sure that your logic is clear between lines!
For more mathematical induction proofs with inequalities, try these:
Inequality Proof Example 1, Σ(k = 1 to n) 1/k² ≤ 2 - 1/n:
• Induction Inequality P...
Inequality Proof Example 2, n² ≥ n:
• Induction Inequality P...
Inequality Proof Example 3, 5^n + 9 lesser than 6^n:
• Induction Inequality P...
Inequality Proof Example 4, n! greater than n²:
• Induction Inequality P...
Inequality Proof Example 5, 2^n ≥ n²
• Induction Inequality P...
Inequality Proof Example 6, [2^(2n)]*(n!)^2 ≥ (2n)!
• Induction Inequality P...
For videos on other kinds of mathematical induction, see my playlist on this topic: • Playlist
I'm Mr. Woo and my channel is all about learning - I love doing it, and I love helping others to do it too. I guess that's why I became a teacher! I hope you get something out of these videos - I upload almost every weekday, so subscribe to find out when there's something new!
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![2^n is greater than n^2. Strategy for Proving Inequalities. [Mathematical Induction]](http://i.ytimg.com/vi/UE009vD3PEI/mqdefault.jpg)
i like the way he teaches. it feels like he's just having a conversation rather than presenting
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.
@@pinklady7184 psychology student
@@pinklady7184 I just think he enjoys his job.
I like his videos but the writing is pretty small, needs to be much larger.
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.
you make my college professor look like an idiot, thanks for helping me pass discrete maths bro :,)
this
my professor makes me look like an idiot. He makes my professor look like an idiot. :)
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.
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 :)
Thank you Eddie for your teachings, your students are truly blessed
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
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!
This is so much more intuitive than the way I was taught. Awesome video.
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!
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!!
You put this up for free viewing! Amazing. Thank you. I will tell people in my class about this channel.
Watching from 2020. I don't understand anything from my online classes in uni. Now I am here and I understand everything. Thank you!!!
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!
Wow, this breaks it down perfectly. Seems so simple and concise. Thanks Eddie!
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
I've been at uni for almost 4 weeks now and this is the first time im understanding this, thanks so much.
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
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!
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
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!!
Thank You so much for this, this was the ONE concept that had driven me up the wall. Thank You.
Really grateful.It was really hard topic to understand and thanks to you I'm finally starting to understand it.
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 !!!
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!
I have been through all the youtube videos for the past week on this topic and now i finally understand.thank you Eddie
Exceptionally articulate. You made a problem that looked complicated on my midterm study guide easy. Thanks a lot :)
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.
This has been the most straightforward explanation! Thank you Mr. Woo, you da real mvp
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 CZcams tutor is 100000% better than those useless PHD professors at my university, they just over complicate simple things, this is so refreshing. Thank You!
I love the energy he puts in the presentation
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.
THAT CLEARS IT UP. I LOVE YOU SIR. KEEP UP THE GOOD WORK!
You made everything SO much clearer. Thank you so much
Thanks A LOT for this! You're a great teacher I finally understood
Been stuck on this for a while, thank you so much for the good explanation!
THANK YOU SO MUCH
THIS IS SO HELPFUL
I never did understand inequalities quite well, but this is pretty concise
This explanation is so much better than the one my teacher gave me!
Thank you very much for uploading this :)
I wish my professor would explain how everything ties together like you do thank you so much for this video this helped so much
wow wow love your energy for teaching and math. Wish I had you as a teacher in high school.
Those who teach, in any capacity, need to take notes on this man. He has a unique understanding of communication that engages the audience.
Awesome video! The last part with the inequality substitution was really confusing until I saw your video!
You've just saved me for an upcoming final! Thank you very much for this!
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.
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!
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.
omg he is so amazing this guy is the best teacher i have ever had in my entire life omggg
Eddie Woo's math skills are so great that he woos many
This helped me so much thank you!! From Ireland 🇨🇮
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?
The GOAT honestly. What a great guy
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.
Thanks so much for a great explanation! Finally understand this!
thank you very much, this is much easier and more logical to follow than the way it is done in my textbook
Algebraic trickery! Thanks for making a hard subject understandable!
Thank you, Eddie. I appreciate your help!
Dude, you're awesome! Do you have some examples with infinite products and binomial coefficient? It's a bit more trickier to deal with those expressions
you are not only a lifesaver but the best maths teacher alive. i am just wandering, which school do you teach at?
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
You just cleared....so many of my doubts! Thanks!
You saved my discrete math final
you're my hero
eddie you're actually a king
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
Thankyou Eddi!!!! Now I love Proof questions!!!
You are a great teacher Eddie! Thanks a lot :)
this man just single handedly safed my maths homework and potentially test
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 ^-^
i appreciate the good work you do for us thanks
thanks a lot for this lesson sir, It is so useful to my studies.
Dude this is so good. THANK YOU
Thanks for the video, this explains it 100 times better than in my textbook :D
Already 2020 but still helped me a lot. Thank you.
Thanks, finally someone explain as needed!
I've never seen a Asian with an Australian accent before. He's hot and smart. Great video.
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!
***** Haha thank you Mr. Woo! And check your direct youtube messages if you're bored and get the chance! =)
***** One teacher to another. You are doing a good job.
I agree, great job. The book didn't explain it nearly as well as you did.
You are my hero! Thank you Mr. Woo!
Very helpfull, Thanks a lot Eddie !
Very good, thank you for explaining how to do these proofs.
literally the best teacher
Nicely done Eddie!
you made that so clear, thank you!!
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.)
Great demonstration. Thanks for posting this; you helped me :)
Great teacher, good job man!!
THANK YOU EDDIE CLUTCH!
From 7:33 to 8:00, my mind exploded!!!!! It all makes sense now!! Thank you sir!!!!
Thanks a lot, I found it very helpful.
Brilliant lecture!
Great video! Thank you Eddie!
Absolute life saver, thank you so much.
Some teachers are a living proof that no concept is hard
Thanks for this! New topic in maths next term so I decided to get a headstart. :)
Omg
Thank you
My teacher could never 👏🏻👏🏻👌🏼
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.
you're great, that was so easy to follow and understand ! thanks!
Nice explaining sir! Thanks a lot! :D you're a great teacher :)
Wow very clear explanation, thank you so much
So helpful, my maths lecturer at the university of Liverpool is terrible at explaining this you made it so simple, thanks!
+Aidan Sullivan Small world. I'm a fresher there now doing Computer Science and now I'm here trying to learn it, haha.
thanks for the video.. its very helpful to me to understand..
The second inequality is actually also true for n=4
4!=4*3*2*1=24, 2^4=16, 24>16
Thanx, I finally understand the two situations. But How do you prove for an inequality where n is the base for example; n^2 >=n. Your response will be highly appreciated!
thank you eddie!!!