Mathematical induction with inequality

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

[bombergame]

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

[adwz]

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

[alpmuslu]

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

[SmilingDiamondRing-jtps]

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

[mdasifeqbal]

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

[markslowhand]

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

[glorrin]

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 <= 2^(n-1)
for n>= 1, it is done in the video
for n <= 0, n-1 <0 so 0 <= 2^(n-1) <= 1
so n <= 2^(n-1)

Oh and finaly, back when I was still at school (a long time ago)
Students tend to confuse "for some k in |N" and "for every n in |N"
changing n into k for this example, I hope makes it more understandable that they are different.

[incognito_tab]

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

[NigusMamo-df]

Thank you for your guidance and support. Your dedication inspires me to learn and grow.

Sincerely, [Thomas]"

[sultangaddafi]

Damn...I was sooo confused but my doubts are now cleared!!...Mathematical proofs can be a unforgiving but thanks to you all's well!!!

[davidbaker]

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!

[digbycrankshaft]

If k+1<=2^k and 2k<=2^k I don't see how it follows that k+1<=2k.

[mady-son]

One of the best videos explaining this topic

[flight]

what we have to prove is the same as "2n <= 2^n", then If we do it differently, we can employ the arithmetic-geometric inequality : x1.x2...xn <= (x1+x2+...xn/ n )^n, we just need to set it up X1=2, X2 = n, X3 =1 so ( n*2*1*1*1....*1) <= (( n + 2 + ( n - 2)*1) /n ) ^ n so 2n <= (2n/n)^n Ultimately, we obtain 2n <= 2^n or n <= 2^(n-1)

[holyshit]

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

[holyshit]

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

[nicolascamargo]

Wow genial esa pasión que le pone a los videos

[jamesharmon]

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

[Nutshell_Mathematica]

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

[ViniciusTeixeira]

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