Hands down the most clear explanation of divisibility induction I've seen. Genuinely thank you and congratulations every single video of yours on induction I've seen holds up as well
You are indeed a Maths sorcerer. I've tried proving this particular question but it seemed almost impossible till I watched this and saw my mistakes. Thanks a lot.
Was doing a pastpaper and it had this question, i was so frustrated because i couldn't get the answer and I'd been trying for hours.... until i found this!. You're literally an angel, Thankyou for this! Your method is way easier...the f(k+1) -f(k) got me confused but now i get it
I actually did not even understand the reasoning behind it. I could write the proofs but didn't understand why induction worked. I remember reading my book over and over. It kept talking about dominoes and I didn't understand. I was able to prove things with it though. The only proofs I really struggled with were the inequality ones, soooo hard for beginners!!
So yes, it felt circular I think. I just remember not understanding why it worked, at all!! I should make a video on that, explaining why it actually works intuitively and mathematically.
@@TheMathSorcerer yes sir, that would be perfect! I am able to prove using the Induction method, but the problem is, that I do not feel it is rigorous, and I do not understand that why does it always seem to work for k+1
what if instead it was a greater than or equal to sign instead of a plus sign? Ive been having problems finding examples where the lhs and rhs are both to the power of K
what does claim mean mathematically saying sir, i often heard that word whenever i see someone proving their argument in math also the other words like trivial etc where all of that words came from sir
Hey I have a similar problem 7 | 3⌃(4n+1)-5⌃(2n-1). So I end up with way bigger numbers going through the problem, 81 and 25 if you test the problem you'll see what I mean, I don't really know what to do with them, any help would be appreciated!
Hands down the most clear explanation of divisibility induction I've seen. Genuinely thank you and congratulations every single video of yours on induction I've seen holds up as well
thank you!
Jeff Bezos before Amazon (without haircut)
Wow I had been stuck on a problem for literally hours. This was the best explanation ive seen. Thank you
You are indeed a Maths sorcerer.
I've tried proving this particular question but it seemed almost impossible till I watched this and saw my mistakes. Thanks a lot.
You are the MVP with math proof content sir, especially mathematical induction. I love it!
THANK YOU SIR!
YOU ARE SO KIND SIR, YOU ARE SUCH A BIG MATHEMATICIAN, BUT ALWAYS SO HUMBLE, THANK YOU!
:):):)
Thank you!!
The "2 blah + 7 blah is 9 blah" had me rolling.
Here is how to proof 3^(2n + 1) + 2^(n+2) is divisible by 7 w/o induction.
3^(2n+1) + 2^(n+2) =
3*9^n + 4*2^n =
3*(2+7)^n + 4*2^n =
3*2^n + 4*2^n (mod 7) =
7*2^n (mod 7) =
0 (mod 7).
Therefore 3^(2n+1) + 2^(n+2) is divisible by 7.
Thankyou so much..
Tomorrow is my exam and u helped me a lot..
Idk the result..
But u gained so much respect
Good luck!
respect to you sir you always make things clear all the way from Africa
wow that's awesome, Africa so cool! Very happy it helped!!
Samina mina ay ay ।
You helped me a lot sir, for my exam. 💕 from India :)
Great way of understanding the concept ..
Love from India
Was doing a pastpaper and it had this question, i was so frustrated because i couldn't get the answer and I'd been trying for hours.... until i found this!. You're literally an angel, Thankyou for this! Your method is way easier...the f(k+1) -f(k) got me confused but now i get it
I just love the way you teach
Excellent sir (from India)
When you first learned proof by induction, did it feel like circular reasoning to you?
I actually did not even understand the reasoning behind it. I could write the proofs but didn't understand why induction worked. I remember reading my book over and over. It kept talking about dominoes and I didn't understand. I was able to prove things with it though. The only proofs I really struggled with were the inequality ones, soooo hard for beginners!!
So yes, it felt circular I think. I just remember not understanding why it worked, at all!! I should make a video on that, explaining why it actually works intuitively and mathematically.
@@TheMathSorcerer yes sir, that would be perfect!
I am able to prove using the Induction method, but the problem is, that I do not feel it is rigorous, and I do not understand that why does it always seem to work for k+1
Mark Dave
Yes buddy!
Best explanation ive seen so far ! Thank you 🙏
was struggling on precalc review... thank you this helped so much
Respect to you sir ......u are great helper ..I'm from Pakistan
Thank you !
you deserve the title math sorcerer
how would you use proof by induction to prove a function is not divisible by a real number, like n^3 +2 for example is not divisible by 8
GIGACHAD THANK YOU MY BROTHER
what if instead it was a greater than or equal to sign instead of a plus sign? Ive been having problems finding examples where the lhs and rhs are both to the power of K
thank you man, you are a genius
I have been looking for so long for this exact kind of question, i messed this up in my exams. Thanks a bunch.
You a great teacher.
Thank you sir
You are welcome!
2:23 did you mean "when n equals k plus one" and not "k plus two?"
what does claim mean mathematically saying sir, i often heard that word whenever i see someone proving their argument in math also the other words like trivial etc where all of that words came from sir
tq for nailing things out, got so much clearer now
Excellent!
Would I be correct if I said that the value of m on the formula b =ma is the base case?
How about for all positive integers n?
What is mean 7m i did not got it
Thank you, great explanation
You are welcome!
if i got 7(9m+2^k+2) as a proof is it ok ? or it just has one solution ?
Brilliant
Wow this was so helpful!
👍
amazing
Legend!!
awesomeee
Thanks so much!!!
You are welcome!
thank you the math sorcerer!
thank you Alex Reynolds!
@@omeedmehrzad6089 Thank you Kate Mehrzad!
Amazing!
thank you
This helped. Thank you.
Thanks sir
beautiful
love from Pakistan
❤️
Tnx sir
Wow
Calculus I !!! :)
😀
👍
Thanks Man
Thx
i love you
Bad teaching
Thx Bro👍
Hey I have a similar problem 7 | 3⌃(4n+1)-5⌃(2n-1). So I end up with way bigger numbers going through the problem, 81 and 25 if you test the problem you'll see what I mean, I don't really know what to do with them, any help would be appreciated!
to further explain he gets 9 and 2 but I get 81 and 25 so it's a bit more complicated