Induction Inequality Proof Example 3: 5^n + 9 less than 6^n

Рет қаралды 123,079

10 жыл бұрын

Another viewer-submitted question. Inequality proofs seem particularly difficult when they involve powers of n, but they can be managed just like any other inequality given the right algebraic techniques!
I had to stop and start this video a couple of times due to the cleaner walking into my staffroom while I was shooting. Hopefully it doesn't interrupt the flow of the explanation too much!

Пікірлер: 107

@sdadasdadsada2993 3 жыл бұрын

Sir you deserve a spot in HEAVEN for this one, literally didn’t get this for the longest time until I stumbled upon this jewel

9 жыл бұрын

Such a good explanation!

@TheTrealistInMemphis 5 жыл бұрын

Awesome explanation, thanks. Made me think about as opposed to blindly following steps that do not always work.

@WillSk8ForFood313 7 жыл бұрын

Just stumbled upon your videos! You are a truly gifted teacher! Thanks so much for sharing this and taking the time to make your videos!

@ernestc.mutalejr1987 3 жыл бұрын

7 years ago you made a video to save my life today

@nickmeyer550 8 жыл бұрын

I'm generally solid with logic problems and proofs, but this one stumped the heck out of me. I re-read my material for hours, searched online, and worked with classmates. I came to a solution, but I was never able to fully understand why it worked, until I found this video. Fantastic explanation, and done in a way that clearly explains the concepts without the viewer feeling stupid. Thank you!

@fieryjack6396 8 жыл бұрын

This is pure wizardry and black magic!:) Brilliant explanation, a real pleasure to follow!

@steveochoa7801 5 жыл бұрын

Amazingly skilled instructor with great demeanor and tone. Easy to pay attention and follow. Wish I could have learned from him in high school.

@mattbenningfield7052 10 жыл бұрын

Didn't understand mathematical induction with inequalities until I watched this video! Amazing job on explaining the individual steps to obtain the end result! Thank you!

@avidgamer699 9 жыл бұрын

To make the last step easier , you could've just added in a new inequality to show what you were saying is true. i.e. 5^(k+1) + 9 < 5^(k+1) + 9 + 5^k + 45 Then from that inequality you could easily show that since: 5^(k+1) + 9 + 5^k + 45 < 6^(k+1) Then 5^(k+1) + 9

@FiftiesDad 3 жыл бұрын

Best description I have seen so far. Thank you very much.

@aaronthompson144 5 жыл бұрын

Wow! This is one of the best examples I have watched!

@Yeldho7 7 жыл бұрын

This man is a godsend. Hoooly, i understand it way better now. Thank you so much!

@knickkennedy 6 жыл бұрын

Cleanest explanation I've found on this topic. Thanks!

@mistbabe26 10 жыл бұрын

Your excellent, please continue to make great videos such as this. This video saved me for my finals which is tomorrow :(. Thank you Eddie!!!

@thineshselva3874 8 жыл бұрын

Thanks mate I have been saved by you !! Keep uploading good stuff like these which are very helpful

@dahudge9 9 жыл бұрын

I'm struggling with my Discrete Maths homework and low and behold this is the exact problem I'm struggling with out of my book. Thanks so much!

@chuckhoush5300 9 жыл бұрын

Holy cow THANK YOU this makes a lot more sense now

@Zaboo 7 жыл бұрын

Thank you so much for your very clear and easy to understand explanation!

@markx3phillies 9 жыл бұрын

my problem was very different but similar enough to the point where i could easily apply your steps and change them to fit my problem. thank you so much!

@ezodragon 10 жыл бұрын

Thank you! Inequality induction is giving me huge troubles and I've finally understood an example.

@dimateo9800 5 жыл бұрын

You are a good teacher bro, it's worth a subscription

@Leftbehind126 10 жыл бұрын

Thank you! I've been struggling with this for a while now!

@kurokatana101 7 жыл бұрын

One of the few videos I've watched that make sense! I may survive discrete mathematics yet!

@OrionRox 8 жыл бұрын

Thank you so much. You explained much better then my math teacher!!

@allyvizcarra8926 3 жыл бұрын

omg king this helped me figure out inequality induction proofs so fast thank you

2 жыл бұрын

Again I paused at the beginning and again I used the trick that if the gap between the two side grows continuously, then the equality will always be true. Here's just the inductive step this time: (5^(n+1)+9)-(5^n+9)

@ibrahimovicyazza8203 9 жыл бұрын

You are an excellent teacher, thanks so much!

@glendenningmichael 5 жыл бұрын

why cant all teachers actually explain the material like this guy?

@Supercatzs 9 ай бұрын

I finally understand inequality proofs now, thank you so much

@luckydog32 7 жыл бұрын

Really great explanation. Thank you so much for this :D

@adnanshafi1481 8 жыл бұрын

Great explanation! Thanks.

@nickshields5982 8 жыл бұрын

Man you just saved my life!

@cliftonmccallum8660 5 жыл бұрын

Thank you for the detailed explanation; I finally understand this.

@shepieces 5 жыл бұрын

so clear and easy to follow and understand....thank you!

@TSkyD 10 жыл бұрын

Awesome stuff! Thanks a lot Sir!

@abdullahirkin 5 жыл бұрын

Very clear explanation, thank you.

@magnusonx1 7 жыл бұрын

BRILLIANT PROOF ! !

@omgiownk 7 жыл бұрын

great explanation thank you so much

@aqeelahmad3472 Жыл бұрын

I really want to thank you sir.🙌🏻🌼

@765cottoncandy 9 жыл бұрын

thanks so much for this video, really helpful. My particular question involved a closed inequality and I wasn't sure if you could use the same reasoning at the end, that if x + a is less than or equal to y then x must be less than or equal to y, since it could never be equal to? But I think since it will always be less than, you can still use less than or equal to sign since either option is valid

@deekshatewari3022 8 жыл бұрын

how do you know when to manipulate the Pk+1 statement or Pk statement to get the answer??

@avi-ventures 7 жыл бұрын

Thank you so much Eddie !

@adityanagesh6309 7 жыл бұрын

The set notation N/{1} can also describe the domain of n

@thelenardjourney8525 5 жыл бұрын

Explained extremely clearly

@margaritakochurova7550 6 жыл бұрын

You're amazing! Thanks!

@cosmickitty9533 7 жыл бұрын

A cool new way of thinking about induction

@prathamagarwal19 5 жыл бұрын

Spreading the beauty of mathematics❤

@benmokgwebo6909 8 жыл бұрын

what is it that u cant explain better? you make maths fun. thank you

@soumyashreeram1012 8 жыл бұрын

such beauty! thank you very much.

@mahboobalam3807 8 жыл бұрын

it's very helpful ,thank you very much

@TheUntitledworks 4 жыл бұрын

I love this man

@abiramn9983 7 жыл бұрын

In Year 9 and got stuck on a similar question, thanks =D

@alireza1505 7 жыл бұрын

waw perfect explanation thank you again

@sblasiol 7 жыл бұрын

This is a great explanation of a confusing subject.

@bladekiller2766 6 жыл бұрын

You saved my life struggle.Just tell me what I owe you.

@Why_so_joe 8 жыл бұрын

I'm in 11th grade and learning this in greek 0.o thank you for the revelation.

@kevinshen2793 7 жыл бұрын

Would it help if I moved everything to the LHS first?

@Bretaigne 6 жыл бұрын

Bless this video

@siralvinmathtutorial Жыл бұрын

Thanks for this video, sir

@Viiiii96 9 жыл бұрын

What happened to the 5^k+1? in 4:40

@apabulldog 6 жыл бұрын

Wow this makes total sense now!!!

@TheGoProGuy07 9 жыл бұрын

Can you please do n! > 2^n, n>=4 !!? Thanks!

@daniel.w8112 3 жыл бұрын

That was Sweet, Thanks

@jasonzhu146 3 жыл бұрын

Excellent!

@naduldissanayake Жыл бұрын

thank u so much mate ❤❤

@Specnutz 10 жыл бұрын

please tell me that there is no one way of solving this. would it have made a difference if i had solved the left hand side first? thanks.

@ruidechen 8 жыл бұрын

Nice video! Really clear and easy to understand! :) I have a question, how do we use induction to prove an inequality that has 3 sides? I got a question that's prove this holds for all positive integer n: 1^3+2^3+3^3+....+(n-1)^3 < 1/4n^4 < 1^3 + 2^3 +.....+ n^3. (the ^ means the power.) I have no idea how to start this off. I get the idea of induction but idk how to prove this.

@34werwe 10 жыл бұрын

Hi, is it necessary to split the 6 into 5+1?

@Workdaily9250 3 жыл бұрын

Thank you Eddie ..

@TechToppers 3 жыл бұрын

Gotcha! Thank you

@gerardo2582 7 жыл бұрын

Great video!

@joelamoako6778 5 жыл бұрын

thank you so much!

@kalaboso01234 3 жыл бұрын

Thank you!

@meganamberr14 7 жыл бұрын

THANK YOU SO MUCH

@solferrari9739 6 жыл бұрын

you're AMAZING

@a.sathyajothi2580 3 жыл бұрын

Thank you sir.

@2cwl4u 7 жыл бұрын

thanks i needed this bc my precalc teacher is terrible

@ruyperezcallejas468 3 жыл бұрын

thank you!

@seanoconnor7029 9 жыл бұрын

you are amazing

@sergebyusajabo2138 6 жыл бұрын

So damn good. Thanks.

@thekillermuffin9557 9 жыл бұрын

Hey what sort of camera system do you use? I was thinking of doing similar videos...

@VenturaPiano 10 жыл бұрын

nice explanation

@arjun-cw7cr 7 жыл бұрын

thanks a lot!

@alvinmath 4 жыл бұрын

sorry what is RTP?

@abood7aj 10 жыл бұрын

nice work

@mikejcooper1 10 жыл бұрын

Hi great video! (5^k +45 >0) why does it need to be greater than 0? at 8:21 mins. Surly as 6^(k+1) is greater than the entire function, it wouldn't make a difference if it was > or < zero. If it was less than, the LHS would be even smaller? thus still true? Example if, 4

@Fightclub1995 8 жыл бұрын

+Mike Cooper 5^k + 45>0 because k is at least 2. If 6^(k+1) is greater than 5^(k+1) +9 + (a positive number), than you can easily conclude that 6^(k+1) is greater than 5^(k+1) + 9. I hope this helped?

@holidaysv2 5 жыл бұрын

ur a legend

@stevencheng7997 3 жыл бұрын

Sir I have a question, how to prove 3^n > 2^n + n^2?

@thelastcipher9135 8 жыл бұрын

if you're writing a book on how to write proofs, please let us know. thank you!!

@wweennddyy17 5 жыл бұрын

holy shit this made sense????? Thank you!

@user-us4ws9px2s 8 жыл бұрын

i rewind 20 times now, still, how do you know that the extra sum doesn it big enough to change to ineqality? you add a positive to a postive so it could pass 6^{k+1}

@thelastcipher9135 8 жыл бұрын

what the video is saying, if 6^(k+1) > 5^k + 9 + (extra sum) then obviously 6^(k+1) > 5^k + 9 with no extra sum. 6^(k+1) > 5^k + 9 is the inequality that eddie woo is trying to prove in the beginning of the video

@Zyhru 3 жыл бұрын

omg I FINALLY GOT IT LMAOO

@PasserbyP 7 жыл бұрын

Eddie what's your setup for recording like this?

@justinlewtp 7 жыл бұрын

Kingportable You can also use a cheap box with 1 open side First, face the open side towards you Second, cut a hole the size of your camera(at least the lens) Third, put a camera on the top(where the hole is) face down and you can write inside the box(presumably a paper or whiteboard) and can reacord with a birds eye view. You may also want to consider puting lighting because it is going to be dark

@PasserbyP 7 жыл бұрын

Haha can you give me a link to a picture to get an idea. What would you call this? So i can google it up. But i think it's a similar idea to a projector. I like it but not sure how to get the lighting working and how to make it so i can right easily while filming.

@brijindersinghmann8707 8 жыл бұрын

2^(n+1) >= n^2 + 2?? please help me sir.

@brijindersinghmann8707 8 жыл бұрын

+Brijinder Singh Mann for n>=0

@demogorgon2125 3 жыл бұрын

Sir would you please give me any hint to solve this inequality problem by induction ~ 2( √( n + 1) − 1) < 1 + 1/√2 + 1/√3 + • • • • + 1/√n I would be highly obliged if you woud kindly help me to solve this...Also I convey my heartfelt thanks for your nice explanation..☺☺

@obyou77 7 жыл бұрын

Can you teach discrete mathematics? lol

@jerrymahajan 4 жыл бұрын

Hi, after multiplying both sides of the inequality by 6: 6(5^k +9) < 6(6^k), could you not say that 5< 6, so 5(5^k + 9) < 6(5^k+9), as k is positive and then : 5(5^k +9) < 6(6^k) 5^(k+1) + 45 < 6^(k+1) as 9 < 45, 5^(k+1) + 9 < 6^(k+1) as required, therefore by p.m.i.....