I love this channel. Im an aspiring mathematician and frequently encounter overwhelming self-doubt about my ability. But when you explain something and reassure the audience that you struggled also, it is uplifting to know that it is not just me struggling with seemingly easy concepts. Seriously, thank you so much for this.

I just had an assignment due today, containing this exact problem. This is a very clear way of explaining it!

@TheMathSorcerer

4 жыл бұрын

Oh wow what a coincidence!!

@ChandanKSwain

3 жыл бұрын

@Kathleen McKenzie yes there mentioned that n>4, but he put k=4 , in the middle equation.....

@bigmansanister8716

3 жыл бұрын

@@ChandanKSwain yea, that confused me as well

@leonbehrndt2611

2 жыл бұрын

@@TheMathSorcerer Same haha

@pranjalsrivastava3343

2 жыл бұрын

he discovered gravity xD

For clarification, I know I am very late to responding to this video, however, when you use k=4 you must be sure that the inductive hypothesis hold for that value of k. If you plug 4 into inductive hyp it actually fails to be true. You must use a value for k that you know the inductive hyp holds true for. In this case it would need to be k=5.

@xreiiyoox

Жыл бұрын

yes exactly, that's the part i was confused at to why he put k= 4 when k is bigger than 4, your comment clarified me thanks

@ayeyukhine466

Жыл бұрын

@@xreiiyoox I think he puts 4 because of < before k^2.

@jimpim6454

6 ай бұрын

What are you talking about its an inequality he didnt 'plug in k=4' he replaced it! I e he threw it in the bin and replaced it with something we know for a fact is smaller than k . Since k is bigger than 4 replacing k with 4 forces an inequality it is him reshaping it so it ends up looking like the conclusion.

You amazed me. I just came from Eddie woo and others for this question now YOU! It’s like you understand the most basic intuition needed to solve it and you did it in so little steps. your solution is gold man. even for the factorial question. THANK YOU SO MUCH

@TheMathSorcerer

4 жыл бұрын

Aww thank you!!

@raymondphiri8587

4 жыл бұрын

So true!!!! You are good🙏🏽🙏🏽

@Hello_am_Mr_Jello

4 жыл бұрын

Same, just came from Eddie

@Qubit313

2 жыл бұрын

same

I've been struggling a great deal in my proofs class and was self-conscious about my ability to think critically because of it. After watching this, not only do I understand the concept, I feel that I have a greater understanding of how a proof proves its claim. Thank you so much for this video, it has helped immensely!!!

Everything's so clear now that I wanna cry oml! THANK YOU!

@TheMathSorcerer

3 жыл бұрын

You're welcome!!

Thank you so much! You really inspire to continue on with school through this math stuff. Sometimes I feel very unmotivated with math because I'll try and I'll try, and when I get it, it's awesome. Plus it's something I genuinely enjoy, so it sucks sometimes when something is just not clicking. Anyhow, I've been watching some of your videos apart from the instructional math ones and they're definitely inspirational, thanks!

This is an extremely good video because you stumbled (or pretended to :) ) a couple times and talked us through how you figured it out. That’s super helpful. Thank you.

@TheMathSorcerer

4 жыл бұрын

😄

@TheMathSorcerer

4 жыл бұрын

Thx😄

I appreciate the intuitive approach you take - so much of PMI instruction involves chaotic jumps in reasoning that are hard for listeners to follow and seemingly impossible to intuit ("how did you know to do that?"), so your decision to work with a problem you didn't already know is a great help. :) I was able to get this one a different way, but I had to use a pretty ugly derivative in the middle; your method is much more elegant.

KZread SHOULD OPEN A SCHOOL FOR ALL THE KZread TEACHERS THAT TEACH BETTER THAN SCHOOL TEACHERS. PERIOD.

@mr.knowitall5019

3 жыл бұрын

@SteveEarl Watt?

@beri4138

3 жыл бұрын

@Eyosias Tewodros Are you a robot?

@schizoframia4874

4 ай бұрын

My ears hurt 🩸

How can you replace the k by 4 if it has to be >4?

@DodiHD

4 жыл бұрын

he messed up there but k^2 + 2k + 10 is still > k^2 + 2k + 1.

@marangelitorres4515

4 жыл бұрын

@@DodiHD I don't think he messed up. He is not saying k=4, the inequality says > k^2+kk, so whatever is on the left side is greater than this. So using 4, we are saying it will be greater than the value obtained when substituting 4.

@CallBlofD

3 жыл бұрын

How you know for sure that it will be greater from the value obtained after substituting with 4?

@isittrueisitnot3303

3 жыл бұрын

I think it goes n>=4 because we had the exact same task like this it was only n>=5 so it's probably a mistake he didn't notice but still correct..

@nyashadzashegava9568

3 жыл бұрын

'CAUSE K》4.

My teacher tried to prove instead that the difference between the inequalities is bigger than zero, I myself find that much more confusing so when I saw this, I was able to solve any problem of inequalities, thanks alot you are going to save my grades.

Love your channel. So laid back and cool. Helping me so much with my math major. Tysm!

@TheMathSorcerer

3 жыл бұрын

You are so welcome!

My prof had 1hr and 30 mins to explain this topic and you nailed it within 9 mins. I understood your explanation better than my prof.

@TheMathSorcerer

2 жыл бұрын

Thx, this is a hard topic to explain! I remember learning this myself and just not getting it. I ended up giving up and only understood it a year later when I looked at it again.

@Amantheparadise

Жыл бұрын

@@TheMathSorcerer looking again,is also a mathematical step ,it works

Aww man, this was beautiful, you were down to earth and showed very clearly all the things I missed from too many conversations with my professor. I actually have a good idea now, of how I should think when doing these inequality proofs. Absolutely amazing. Thank you!!

Thank you very much for your videos. Do you have a good book that really tackles inequalities to have a mastery in them?

Hi may i ask what property or theorem you used when you replaced 2^k to k^2?

This was amazing. Thank you so much. This is the 8th place I visited trying to find an intuitive explanation.

@TheMathSorcerer

3 жыл бұрын

Excellent, glad I helped😃

That was so cool. I am barely starting my classes for my degree and I understood nothing, but it was very cool seeing you work out the problem. Some day I’ll get it.

@okohsamuel314

Жыл бұрын

vashTX ... U said "some day I'll get it" ... meaning, u still haven't gotten it.

Wow, thank you so much! Excellently explained and easy to understand after you think about it a bit.

This was extremely helpful after weeks of struggling. Thank you very much. :D

@TheMathSorcerer

4 жыл бұрын

Excellent!

never saw a more enthusiastic teacher on youtube 👍

So my instinct would be to pivot once you get to the “>k^2+k^2" to proving that k^2>2k+1 for all k>3. I wonder if there is any downside to that method; specifically in how that approach of basing the proof off of another lemma may fail when it is a more difficult problem and perhaps the dependency I need is harder to prove. Any thoughts?

@TheMathSorcerer

4 жыл бұрын

that works but, it's also more work;) but yeah that could work!

@tonyhaddad1394

2 жыл бұрын

Read my comment its easy i just proove it

I can't say how helpful this was. I will now be ready for class tommorow. THANKS!

As the problem says n > 4, should we not use 5 instead of 4 in the inductive step? At 6:42

Thank you so much for doing this video, I’ve been trying to understand this for weeks

great video!! thanks for sharing your knowledge. I have a question related to the substitution done in the minute 5:00 of the video. You said that "..you allow to do that (the substitution of 2^k by k^2) in math" and change the '=' symbol by '>'. I really want to understand how this substitution is possible and I want to know if you could provide us with any reference or material in which we could go deeper into this subject. Thanks in advance and again, thanks for sharing.

@jimpim6454

6 ай бұрын

Its because he is replacing 2^k with something he knows is smaller than it namely k^2 so obviously the equality does not hold anymore so he must write the greater than symbol.

Thank you for your video. K have a question... why does the 8 becomes 1 in the last part?

how do you use the same method for 4^n > n^3 for all N . I try to open it up like that and got stuck at 4^(k+1)>= k^3 +3K^2 .k

genius! I don't know how to thank you, I was in a trouble and this video saved me, a lot of thanks again..

@TheMathSorcerer

3 жыл бұрын

You are welcome😃

Where did the 2^1 gone to?

How did you replace k with 4 when you're assuming for some k>4? Aren't you supposed to replace k with a number greater than 4 because its not k >= 4?

What a smooth proof and explanation, simply wonderful, i love induction as I loved this video!!

Technically this is true for the open interval (4, infinity), so you need a more generalized induction that utilizes the well ordering relation.

2:50 /3:20 /4:47 When dinosaurs roamed the planet xDDDD I love the humility. These are starting to click for me and it's exciting to mess with algebra like this

I see other induction inequality videos that show a different method. I find this method much more comprehensive. Would it work for all induction inequality proofs?

@TheMathSorcerer

4 жыл бұрын

Yes, absolutely, the ideas are the SAME for most of these!! thank you glad it was helpful, induction inequality is so hard to learn!!

Thank you. I was stuck on the '2^1 x 2^k' for a really, really long time. Induction is tough, and I am really overwhelmed but this video has helped me feel better.

Fantastic! Around 5:00 you managed to easily explain what our professor has been failing to...

@TheMathSorcerer

3 жыл бұрын

👍

If k>4 why do we put 4????

Thank you so much. After I see the solution to a proof question that I don't know how to do, I'm always wondering to myself, "how the heck was I supposed to know to do that?" Do you have any tips?

Thanks for the vid I've been struggling with this for ages. I'm a bit confused about where you substituted in 4 for k. How does that work like would it still cover all the values bigger than 4?

@TheMathSorcerer

4 жыл бұрын

I used to struggle with your question also, tons of people do. The simple answer is that it's because k >= 4, so you can make that substitution. For example say k >= 4. And say you have 3k + p then you can write 3k + p >= 3*4 + p = 12 + p that's allowed:) You could work it out the long way. We have k >= 4, so 3k >= 12, so 3k + p >= 12 + p but nobody does that, because it's too much work. So in general, we just substitute as above.

@CallBlofD

3 жыл бұрын

Thank you for your help! Can you explain why k>=4 instead of k>4, because at start it define as k>4, how you change it to also be equal, or on what you depend when you say it. Thank you!

@Chrisymcmb

2 жыл бұрын

@@CallBlofD I was also wondering about this. The problem states that k>4, not k>=4, so that is why I was wondering how the k could be substituted by 4

Here something i don't understand , here a condition that n>4 . How to you put 2×4 replacing by 4k?

First of all, thanks for the video everything is more clear now. Today I had my first exam at college and I had to proof that if A is a countable set then so is A^n by induction. Can you make a video of that?

@TheMathSorcerer

4 жыл бұрын

Will try thank you for the idea!!

thanks sir for the solution I was stuck on this question from last 3-4 hours. great help.from india.

@TheMathSorcerer

4 жыл бұрын

👍

I really liked this method, thank you for your effort .

A saving grace for discrete math this semester :)) Sets theory proofs and now I found out you do induction too, LETS GOOO!!! I was wondering since we were working with k > 4 how you were able to substitute k = 4 into the equation. Because of the I.H it is totally plausible to do this but it would have to be k >= 4. Even for k>=4 this should work right? I assumed since k > 4 that we were only allowed to plug in 5 or greater for k since our I.H is greater than 4 not equal to it. Thank you!

@sebastianohajda411

2 жыл бұрын

I think because for the rule k>4, if we substitute k=4 in the LHS equation, then we know the LHS will be bigger than the substituted version of it because of the rule k>4. I think you can also you k=5, but then you have to use >= sign, since LHS can be bigger or equal to k=5 substituted version of it

Thank you for this tutorial, I was struck with this question, and your video helped me understand. :>

The people want more induction proofs! Please do lots of them. (more tricky ones too)

@TheMathSorcerer

4 жыл бұрын

😄👍

how can you replace 2^K with K^2?

Best explanation I heard. First I thought this problem and my assignment from my pre-cal class was the same but it was actually the opposite " Prove n^2 > 2^n for n >= 5 " After watching the vid, I knew that the statement is already false so how do I show that the statement above is false using The Mathematical Induction?

This is amazing, I was given the first question to work out. Thanks 😍

I thought K was large than 4, so shouldn't you substitute with 5 instead?

i did not get why i can replace k with 4, can someone explain to me?

Wait so how did the 8 turn into one

I am a bit confused. You replaced a k with 4 (I assume because that is the lowest value it can take ). Shouldn't the domain be k greater or equal to 4 in order to use four in the proof? It works with 5 as well, I am just curious as to whether this is a simple mistake or if I don't understand something. Can someone help?

@gunarajregmi6727

Жыл бұрын

I am also confused on it . You can't use 4 . We have to start with 5

@ibghxr

Жыл бұрын

I think he made a mistake, it was 5 imo.

How do we replace the 8 with 1? Why is that legal?

I took discrete math 1 year ago. I didn't understand mathematical induction. This semester I am taking theoretical CS and mathematical induction is needed so I am learning it again. This is the first time I understood a proof by Mathematical inducton.

@ruantristancarlinsky3851

3 жыл бұрын

Lol me too which University

why can you replace k with 4?

Good. I've been in need of just this information.

@TheMathSorcerer

3 жыл бұрын

Glad it was helpful!

Hi there, sir. I find your explanation very clear. I have a project in school, may I use this video to help students learn induction proof. Thanks for your help.

Excellent way of explaining. Night before the submission date. Thank you Sir

@TheMathSorcerer

3 жыл бұрын

You are welcome!

Great video keep them coming. I remember i had the same assignament. Proof was for n>=3 in my case.

The lower bound is like -0.7666647 ish. What is that?

"when I was learning this stuff thousands of years ago..." the stories are true. he is a sorcerer......

@nyashachikomwe8255

2 жыл бұрын

😂😂😂I laughed hard, oh boy🤣

at 6:24 we are claiming that (k^2) + (k^2) > (k^2) + (k*k), but shouldn't those be equal??

I don't know, how you placed 4 at the value of k, as it is mentioned that n >4....

Thank you for your help bro. You're awesome 😎

Thanks for doing this! Cheers!

@TheMathSorcerer

4 жыл бұрын

You are welcome!

How did he go from +8 to +1 at the end? I still don't follow? we're suppose to set it to equal to each other?

@jonathanwu5245

2 жыл бұрын

Okay, I think it makes slightly more sense since 8 is greater than one

very cool to split it up, and yeh is a great look at proofs

I don't understand why we replace K with 4 we have K is bigger than for not equal , so I don't get this point

thank you very much. This helped me a lot :)

@TheMathSorcerer

3 жыл бұрын

You're welcome!

Excellent tutorial indeed!

Since the question doesn't explicitly mention only integer values of 'n', wouldn't it be more approapriate to solve it for rationals? Induction wouldn't be possible but maybe something involving the right hand limit of 4?

@TheMathSorcerer

4 жыл бұрын

it's supposed to be for integer values, oh hmm for noninteger values? I dunno I'd have to think about that one!!! Maybe what you say would work yes, not sure:) I think maybe subtracting it, and writing it like 2^x - x^2, then calling that f(x), and using some calculus, that might do it, maybe!!!

@MrTrollNerd

4 жыл бұрын

@@TheMathSorcerer I thought about it: both functions intersect at x=4, and the derivative of the 2^x term is always greater than that of the x^2 term for x>4. So it becomes trivial, I suppose. It probably doesn't make sense to make it more formal

At 7:33 he has k^2 + 2k + 1. Shouldn't it be k^2 + 2k +1 + 7? If not how did he get rid of the 7?

@mariamihab9542

3 жыл бұрын

Why 7 ?

Sir i need your help plz

wow, you made this problem much easier. thanks

U are the first to teach very well me math induction thx a lot my broyher

@TheMathSorcerer

3 жыл бұрын

You are most welcome!

7:31 "Boom" the moment of enlightenment.

I got completely lost when you suddenly replaced 2^k + 2^k with k^2 + k^2, I have no idea how or why that was done, and everything thereafter made no sense to me. I would really love it if someone could explain what happened to me, I re-watched the video like 4 times. And since when can we just start replacing variables with numbers of our choosing? I'm so lost.

Great video! The only thing I did not understand in the demonstration is why did you replace k with 4? if the hypothesis says it must be > 4 then shouldn't k be replaced with 5? Thanks a lot.

@matko8038

Ай бұрын

If you plug in k=5, the inequality will not hold. We want k^2+k*k to be greater than k^2+X*k. Our original assumption is that k>4 so we have to use some X that is less than k. k^2+k*k > k^2+X*k --> X4 we can use X=4.

I'm quite confused, how is 8 the same as 1? can you please help me?

@marangelitorres4515

4 жыл бұрын

The conclusion that was reached was that 2^(k+1)>k^2+2k+8. If this is true, then it must me true that 2^(k+1)>k^2+2k+1. Eight is greater than 1, so if you have something that is greater by 8, it must be greater by 1. Hope this helps.

At 4:56, I don't understand why we're "allowed" to replace 2k+2k with k^2+k^2.

why do we replace the 8 with 1 near the end??

@yeahno2466

3 жыл бұрын

I'm also confused lol

Good sort of information you delivered to the viewers.

@TheMathSorcerer

3 жыл бұрын

Thx

I don't get how we are writing 4 if k>4, why not 5 like in the basic step 😩 someone please explain

I applied an inductive hypothesis for the original induction hypothesis and it seemed to work better

More please...

@TheMathSorcerer

4 жыл бұрын

Will do!

This deserves a big fat LIKE

@TheMathSorcerer

3 жыл бұрын

Haha thx

So we know that k > 4 is true in the hypothesis step. In the induction step, since n = k + 1, isn't it : n > 4 => k + 1 > 4 => k > 3 ?

@maxamedaxmedn6380

3 жыл бұрын

Oh thanks I think k>3 makes sense Because i was a hard time understanding why he used k=4 In the induction step and at the same time he says k>4

Thanks Jef!

first time I've actually seen you do some actual math(s) but it's still big on the dry humo(u)r

i dont really get it why reaplaced k = 4

First thing I thought of was proving that the equation for 2^n approaches infinity faster than n^2 using the derivative. Didnt know what induction was at the time though

Good job man

Sir,but it's k greater than 4,not k greater than Or equal to 4,might I know why did you put 4 as the value of k, kindly reply.

How I did: Checking base case is easy... I proved another inequality before that: 2^m>2m+1 (for m>4) Make hypothesis and other stuff... To proof: 2^m+2^m>2(m+1)+1 (m>4) This reduces (by hypothesis) 2^m>2 (m>4) Works! Nice! Now to the main thing: Do hypothesis and base checking... To proof 2^n+2^n>(n+1)²=n²+2n+1 This reduces to(by hypothesis): 2^n>2n+1 Proved above! So, hence proved. I suppose. Is that right? I wrote it informally... Would do better in exam... I should have gone the other way round like first write 2^k>k², add inequality I proved and then proceed. You can spare me on KZread right?? And tell if this is right... Please? Will you marks in exam? Or in spirit of math, is the idea correct?

why did you replace the 8 for a 1?

@matko8038

Ай бұрын

because it gets us to prove our claim.

mehn.. i like the way you teach.. better than my lecturer.. lol

Wow thanks!