Mathematical induction with inequality

Рет қаралды 25,790

Prime Newtons

8 ай бұрын

In this video, I showed how to do a mathematical induction proof.

Пікірлер: 68

@bombergame8636 8 ай бұрын

The passion this man has is unrivalled, amazing to watch!

@ycong4689 8 ай бұрын

This man is👍👍👍👍

@SmilingDiamondRing-jt5ps 12 күн бұрын

I really love this man he is the best maths tutor I have ever seen

@adw1z 8 ай бұрын

I love the diversity of the questions u cover, from simple high school to undergraduate to Olympiad material. Keep going, and never stop learning!

@alpmuslu3954 8 ай бұрын

Guys remember to like the video, that’s the least we can do to thank him

@markslowhand4214 4 ай бұрын

A world full of teachers like you would solve a lot of problems, not only mathematical problems!

@davidbaker5725 Ай бұрын

Thanks for this video, it really helped me learn how to better phrase some things when teaching mathematical induction, Your videos are super well done, and really stress the important points of each topic, I appreciate your awesome positive energy!

@PrimeNewtons Ай бұрын

Glad it helped! Thank you for you message. I appreciate it too

@mdasifeqbal2323 7 ай бұрын

This man is better than any class teacher and private tutor.

@Hatsumisen41 7 ай бұрын

Totally agree

@glorrin 8 ай бұрын

Great video :) Here is a funny trivia: in my country |N include 0, and if we want to exclude 0 from any group of number we add a*, so all natural numbers would be |N*, that means it is also easy to define the domain of 1/x which is |R* The example is great to explain induction but we can go further, it is easy to prove that n = 1, it is done in the video for n

@PrimeNewtons 8 ай бұрын

Nice observation. I'll take note

@user-kv4pi2gk3b 2 ай бұрын

Thank you for your guidance and support. Your dedication inspires me to learn and grow. Sincerely, [Thomas]"

@incognito_tab43 5 ай бұрын

Your voice ❗️it literary compels me not only to learn but to understand idk how describe it but tysm for choosing to do this

@mady-son 5 ай бұрын

One of the best videos explaining this topic

@carlosangulo2888 8 ай бұрын

I love your videos bro. Thanks.

@user-yx4du4ii6r 5 ай бұрын

The Best explanation there exist❤

@abdulkhadarainur4348 8 ай бұрын

Never disappoints.

@nicolascamargo8339 8 ай бұрын

Wow genial esa pasión que le pone a los videos

@flight7218 8 ай бұрын

what we have to prove is the same as "2n

@biswambarpanda4468 8 ай бұрын

Wonderful sir

@uwuowo7775 8 ай бұрын

I love your content bro

@holyshit922 8 ай бұрын

About your algebra video series You can mention about similar matrices,Cayley Hamilton theorem, and maybe Jordan form after you finish with eigenvalues you can record something about rotations , reflections , orthogonalization

@dirklutz2818 4 ай бұрын

You're the best!

@Nutshell_Mathematica 8 ай бұрын

Amazing can u set of questions these type in a another video

@holyshit922 8 ай бұрын

1:29 This is one of the reasons I like math For examle when I used to go to school Pluto was consider a planet now it isnt

@PrimeNewtons 8 ай бұрын

I agree

@AZALI00013 8 ай бұрын

very nice video !!!

@davidemmanuel9418 6 ай бұрын

Beautiful ❤️

@ramizhossain9082 7 ай бұрын

Great proof.

@jamesharmon4994 7 ай бұрын

My faith in math is shaken by proofs such as: The sum of all positive integers is negative one twelfth.

@reamartin6458 8 ай бұрын

This was cool 😎 thanks

@ViniciusTeixeira1 4 ай бұрын

I solved the induction step like this: Considering that there exists a natural number K such that K ≤ 2^(K - 1), then K + 1 ≤ 2^(K - 1) + 1. Naturally, 2^(K - 1) + 1 ≤ 2^(K - 1) + K. But by the initial hypothesis we know that 2^(K - 1) + K ≤ 2^(K - 1) + 2^(K - 1) = 2^K; therefore, K + 1 ≤ 2^K

@Vengeance-yb8lm 8 ай бұрын

Do you have any advice for math youtubers who are just starting out ?

@digbycrankshaft7572 8 ай бұрын

If k+1

@danielschneider9358 8 ай бұрын

It wouldn't follow from that, correct. But: The fact that k+1

@coolblue5929 8 ай бұрын

I have the same problem. Surely you can only make the right hand side bigger, not smaller.

@danielschneider9358 8 ай бұрын

The idea here is that you are making an even STRONGER condition, and saying that if that condition is true, the other one also has to be true You want to show: k+1

@martynpage1794 8 ай бұрын

Is it that k+1

@coolblue5929 8 ай бұрын

@@danielschneider9358 you are making the condition WEAKER, not stronger. If you are trying to show that a

@OscarKanyimbo 8 ай бұрын

Thanks 🙏 I'm just having my exam in the next 24 hrs

@Thachoanhdi 8 ай бұрын

We can use Bernoulli’s inequality

@holyshit922 8 ай бұрын

Why induction works ? In my opinion it is based on structure of natural number each subset of natural numbers has minimal value each natural number has successor

@adw1z 8 ай бұрын

It’s like a domino effect. You’ve shown that if it works for some natural number k, it will work for k+1. This in turn means that it will work for k+2 etc… (and so it will work for all natural numbers >= k ) but you’ve shown it works for 1. Thus it must work for 2, then 3, then every natural number after

@yasir6347 6 ай бұрын

Yeah I think that’s the well ordering principle

@tuhinrezareza6966 6 ай бұрын

For 6

@youssefnidhsain4082 8 ай бұрын

i have a question isn't 0 a natural number ? in addition to that p(n=0) is a true statement since 0

@dakehami 5 ай бұрын

0 is not a natural number

@dakehami 5 ай бұрын

0 is not a natural number

@ZANBA_MYON 7 ай бұрын

At 11:30 I didn't see the reason for the conclusion that k + 1 = k + 1 and hence make the connection k + 1

@PrimeNewtons 7 ай бұрын

How did you know 2k

@ZANBA_MYON 7 ай бұрын

@@PrimeNewtons you got a point there. What I could have said was that our induction step assumes that the statement k

@cyruschang1904 7 ай бұрын

if n ≤ 2^(n - 1) 2^((n + 1) - 1) = 2^((n - 1) + 1) = 2 x 2^(n - 1) ≥ 2 x n but 2 x n = 2n > n + 1 (because 2n - (n + 1) = n + 1 > 0) So we have established if n ≤ 2^(n - 1) 2^((n + 1) - 1) ≥ n + 1

@coolblue5929 8 ай бұрын

Sorry, I think your last step is wrong. You can only make the RHS bigger, not smaller.

@PrimeNewtons 8 ай бұрын

Okay

@user-fg9ei1kz9p 6 ай бұрын

why?

@Aiellosfetano 4 ай бұрын

Sorry, i don’t understand why k+1 is < or = a 2k?

@YihuneKifle-zl7np 5 ай бұрын

Bro,solve this mathematical induction question 3^n≥n^2,for all natural number,I need this question answers.please!

@waxis9153 8 ай бұрын

Is math the most trustworthy science? Wel since it's based on certain axioms, as long as we can't prove that those axioms are true we can't really know if math is 100% trustworthy. But then again most of our systems that we have are at a certain level based on axiom(s).

@muhammadnawab3959 7 ай бұрын

At 5.15 u proved that 1 and 2 are natural but u did not say anything about 3

@sparshsharma5270 8 ай бұрын

To be honest I never liked proof by induction. Among all different types of proofs, the proof by induction is said to be the weakest one actually.

@DBstudios98 4 ай бұрын

By who? Induction is not "weaker" than other forms of proof. It's just as mathematically valid as other methods, if it gave less of a correct result it wouldn't ever be used

@sparshsharma5270 4 ай бұрын

@@DBstudios98 All proofs give correct result hence the name. But there are types of proofs with their methods. As per experts, induction is weakest yet most interesting. And as per them, proof by brute force would require all exhaustive cases checked hence large complexity. Like if chess would ever be solved, it would require brute force algorithm. Even for quantum computers, solving chess would take lot of time.

@jafarmasuha268 3 ай бұрын

There are arguments that are not logically accurate.

@jafarmasuha268 3 ай бұрын

The explanation is not logically accurate, so it is difficult for students to understand.

@PrimeNewtons 3 ай бұрын

You need to state what is accurate or inaccurate. Your comment s not helping me learn anything from you. I'd appreciate if you post something helpful 🙂