In this video, I showed how to do a mathematical induction proof.
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@bombergame86368 ай бұрын
The passion this man has is unrivalled, amazing to watch!
@ycong46898 ай бұрын
This man is👍👍👍👍
@adw1z8 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!
@alpmuslu39548 ай бұрын
Guys remember to like the video, that’s the least we can do to thank him
@SmilingDiamondRing-jt5ps18 күн бұрын
I really love this man he is the best maths tutor I have ever seen
@markslowhand42144 ай бұрын
A world full of teachers like you would solve a lot of problems, not only mathematical problems!
@mdasifeqbal23238 ай бұрын
This man is better than any class teacher and private tutor.
@Hatsumisen418 ай бұрын
Totally agree
@davidbaker5725Ай 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!
@PrimeNewtonsАй бұрын
Glad it helped! Thank you for you message. I appreciate it too
@glorrin8 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
@PrimeNewtons8 ай бұрын
Nice observation. I'll take note
@incognito_tab436 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
@user-kv4pi2gk3b2 ай бұрын
Thank you for your guidance and support. Your dedication inspires me to learn and grow. Sincerely, [Thomas]"
@mady-son5 ай бұрын
One of the best videos explaining this topic
@carlosangulo28888 ай бұрын
I love your videos bro. Thanks.
@biswambarpanda44688 ай бұрын
Wonderful sir
@user-yx4du4ii6r5 ай бұрын
The Best explanation there exist❤
@nicolascamargo83398 ай бұрын
Wow genial esa pasión que le pone a los videos
@abdulkhadarainur43488 ай бұрын
Never disappoints.
@Nutshell_Mathematica8 ай бұрын
Amazing can u set of questions these type in a another video
@uwuowo77758 ай бұрын
I love your content bro
@holyshit9228 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
@dirklutz28184 ай бұрын
You're the best!
@AZALI000138 ай бұрын
very nice video !!!
@holyshit9228 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
@PrimeNewtons8 ай бұрын
I agree
@davidemmanuel94186 ай бұрын
Beautiful ❤️
@ramizhossain90827 ай бұрын
Great proof.
@reamartin64588 ай бұрын
This was cool 😎 thanks
@flight72188 ай бұрын
what we have to prove is the same as "2n
@digbycrankshaft75728 ай бұрын
If k+1
@danielschneider93588 ай бұрын
It wouldn't follow from that, correct. But: The fact that k+1
@coolblue59298 ай бұрын
I have the same problem. Surely you can only make the right hand side bigger, not smaller.
@danielschneider93588 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
@martynpage17948 ай бұрын
Is it that k+1
@coolblue59298 ай бұрын
@@danielschneider9358 you are making the condition WEAKER, not stronger. If you are trying to show that a
@jamesharmon49948 ай бұрын
My faith in math is shaken by proofs such as: The sum of all positive integers is negative one twelfth.
@Vengeance-yb8lm8 ай бұрын
Do you have any advice for math youtubers who are just starting out ?
@OscarKanyimbo8 ай бұрын
Thanks 🙏 I'm just having my exam in the next 24 hrs
@ViniciusTeixeira14 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
@tuhinrezareza69666 ай бұрын
For 6
@Thachoanhdi8 ай бұрын
We can use Bernoulli’s inequality
@holyshit9228 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
@adw1z8 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
@yasir63476 ай бұрын
Yeah I think that’s the well ordering principle
@youssefnidhsain40828 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
@dakehami5 ай бұрын
0 is not a natural number
@dakehami5 ай бұрын
0 is not a natural number
@Aiellosfetano5 ай бұрын
Sorry, i don’t understand why k+1 is < or = a 2k?
@coolblue59298 ай бұрын
Sorry, I think your last step is wrong. You can only make the RHS bigger, not smaller.
@PrimeNewtons8 ай бұрын
Okay
@user-fg9ei1kz9p6 ай бұрын
why?
@ZANBA_MYON8 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
@PrimeNewtons8 ай бұрын
How did you know 2k
@ZANBA_MYON8 ай бұрын
@@PrimeNewtons you got a point there. What I could have said was that our induction step assumes that the statement k
@YihuneKifle-zl7np6 ай бұрын
Bro,solve this mathematical induction question 3^n≥n^2,for all natural number,I need this question answers.please!
@cyruschang19047 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
@waxis91538 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).
@muhammadnawab39597 ай бұрын
At 5.15 u proved that 1 and 2 are natural but u did not say anything about 3
@sparshsharma52708 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.
@DBstudios984 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
@sparshsharma52704 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.
@jafarmasuha2683 ай бұрын
There are arguments that are not logically accurate.
@jafarmasuha2683 ай бұрын
The explanation is not logically accurate, so it is difficult for students to understand.
@PrimeNewtons3 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 🙂
@jacktut25903 ай бұрын
please help me solve this Show that 5^n +6^n < 9N for n greater or equals 2.