This guy is so clear in everything he says. Most teachers would skip most of the stuff he's explaining because they feel it's obvious. Khan never assumes that anything is obvious and that is why his videos are so easy to follow.
@royalbuchanan333 жыл бұрын
Facts
@rasibn3 жыл бұрын
Amazing
@psyberpirate3 жыл бұрын
teachers who explain like this are the best ones! The world would be a much easier place if only teachers wouldn't assume that we know the "obvious" things in life. What is obvious to a professor, with a Ph.D. might not be so obvious to a college kid on his first day on the topic.
@azazel703 жыл бұрын
Straight facts
@crimsonsm47682 жыл бұрын
Completely disagree. He explains the problem very well, but the concept itself is impossible to grasp using this video
@F0A0Y0N0U0S9 жыл бұрын
After muddling through my discrete structures textbook, it is so nice to find 9 minutes and 22 seconds of clarity.
@mrinalinighosh95738 жыл бұрын
yess true!! I finally understood in under ten minutes what the teacher couldn't do in a week
@KatrinaSock7 жыл бұрын
You are so right. My DS text talks like a politician. It explains things and then you're really confused.
@jonathansum90847 жыл бұрын
This is how all my Math professors are.
@empiremay7 жыл бұрын
agree.
@andrewjager61776 жыл бұрын
Unbelievable how confused I was vs how confused i am not now
@danielgrobbelaar96729 жыл бұрын
For what it's worth, you've managed to teach in 10 minutes what most teachers cannot do in an hour.
@jamesspacer79943 жыл бұрын
I just spent about an hour looking at proof by induction in an Elementary Linear Algebra book as well as some notes online from Stanford but both of those sources were a million miles away from this level of intuition! Khan Academy to the rescue! Thank you good sir, very clear, understandable and intuitive.
@idknuttin9 жыл бұрын
proving something by mathematical induction isnt that difficult, its the question my professor assigns, he has us proving these ridiculously long sums that requires so much algebraic manipulation that it just makes the problem extremely difficult
@materialknight2 жыл бұрын
So, to prove by induction that an equation is true for all inputs: 1. Check that it is true for the first input. 2. Write the equation, and incorporate (k+1) to both sides by following the pattern of the left-side part. For example: In the video, since the left-side part was a series of additions, (k+1) (the next number in the series of additions) was incorporated by ADDING it to both sides. 3. Transform the right-side of the above equation into the form of the original right-side. For example: In the video, the original right-side is a fraction whose numerator is the input * (the input + 1), & the denominator is 2; that's its form. And the proof merely consisted in adding (k+1) to both sides and transforming the right side into the same form of the original right side (a fraction whose numerator is the input [which in this case is k+1 instead of just n] * (the input + 1), and whose numerator is 2).
@tubasmash13 жыл бұрын
THANK YOU FOR: the colors, the explanation, making me feel better, being great at what you do.
@jcmschott18952 жыл бұрын
That's what teaching should be about: making people feel confident about a subject, from the lowest level up!
@user-cv8xu2yk7m2 жыл бұрын
As a sixth grader whose already learned some trigonometry and calculus from Khan Academy, I would agree.
@weneverforgetwearelegion10 ай бұрын
@@user-cv8xu2yk7mhahahaha cap
@Dirk_Bergamot9 ай бұрын
Yeah, talk about great..
@moonmilk1510 жыл бұрын
Thanks again Khan, I can watch your video and understand it. You're making the world a better place. You would not believe how much better this is than my class.
@thaiduy23467 ай бұрын
It has been 13 years since the video was posted, but the value it brings to new generations like me is legendary and immortal. Thank you!!
@jonasalbaira8969 жыл бұрын
buddy you are god's gift
@yamahrahda8 жыл бұрын
IKR!!! This, just kept me from failing math class.
@abodalashkar56865 жыл бұрын
@@zeyres4029 you're his mother?
@spookimiiki58914 жыл бұрын
fell off the wagon on my zoom course, muted the presentation, watched this at 1,5x speed and I was up to speed. Great video!
@JalebJay13 жыл бұрын
I remember the story of how this formula was made. The creator of the proof was causing problems in class and his teacher told him that he had to find the sum of every number between 1 and 100. He started to notice a pattern when he added 1 and 100, 2 and 99, 3 and 98... seeing that he is getting 101, 50 times. So he showed it to his teacher saying the answer was 5050. The teacher didn't believe him and wrote out the whole problem and her results came out equaling 5050.
@dacrecapstick511411 жыл бұрын
So well explained, and i like the fact you say things multiple times! Helps it stick in my head. thank you very much.
@xiexiefrank210 жыл бұрын
omg this is so much better than my lectures, i question why i pay so much money to go to lectures where i get very lost. my math proofs prof sucks balls i don't understand shit when she explains but everything is so clear now that this guy explains it
@armunalam9 жыл бұрын
you can also visit the official website (www.khanacademy.org/) to get the full list of subjects!!!!!!!!!
@mumsazpatel97596 жыл бұрын
4 years later and ur comment is still relevant
@macho77vg3 жыл бұрын
@@mumsazpatel9759 6 years later and the comment is still relevant.
@Chandler8907 жыл бұрын
the factoring out k+1 got me weak
@abekor705 жыл бұрын
think "FOIL"
@williamshorrock-browne59995 жыл бұрын
I think he's saying 'it's got him weak at the knees' as in, he enjoyed it.
@NoActuallyGo-KCUF-Yourself5 жыл бұрын
Factoring is your friend. 😊
@spaceghost83275 жыл бұрын
*bruh your comment got me weak haha*
@JavierRodriguezTX4 жыл бұрын
check out factoring my grouping
@joealewis4121 Жыл бұрын
I should just pay you instead of paying for college courses. U explain everything perfectly.
@StuhFu13 жыл бұрын
Thank you soo much Khan! Everybody thinks they know how to explain this but they rarely tie it up so that it makes complete sense.
@KingUnity225 жыл бұрын
That reveal at the end blew my mind. I didnt even realize that he had exactly rewritten the original formula.
@elijahsokoni79975 жыл бұрын
WOW!!! This is definitely something else. The examples are always easier than the task. We're having a test today and this is killing me.
@tadalamanda98772 жыл бұрын
After multiple fruitless attempts to understand this concept, I finally get it. Thanks 🙌
@KickOff_Kreations7 ай бұрын
This video just solved all my doubts. Always grateful for your videos.
@nastarankianersi1042 ай бұрын
This reminded me of the good old days back in high school when I was the straight-A kid in the class. Didn't think I would forget proof by induction someday, and didn't think I'd need it in software engineering (Automata theory course). Thanks a lot
@fernandogameyt7632 жыл бұрын
Wow he is way clearer than my teacher. It's amazing.
@eliyoung9406 Жыл бұрын
Lol
@DominicI1 Жыл бұрын
Thank you. This explained proof by induction to me with the same example as my professor but 1000x easier to understand. No steps were skipped. Again, thank you
@amberglaze9098 жыл бұрын
In my introduction to higher mathematics class, MTH 311, I can pay attention for like the first 30 mins. Then the next 30 mins I'm either staring at him write a proof on the board while thinking about what I want to get from the vending machine when class is over, or how I'm gonna even attempt to write anything on the next assessment, or anime. Or sleeping. The the last twenty mins we take an assessment where we have to write a proof on what we learned that day and two days ago.
@Dirk_Bergamot9 ай бұрын
As far as KZbin math tutoring videos go, not rewinding once, like watching this video: practically impossible.
@alhussein_alahmed_lnu Жыл бұрын
thank you very much! i have been struggling with this for the past 2 weeks now I think I get it!
@amritraj68653 жыл бұрын
Oh god ! I was totally intrigued about this topic. Another people were just teaching me how to solve problems based on it. None of them teaching me how it works. Hats off⚡⚡
@zachv74495 жыл бұрын
I don't know how they do it. I go into a video confused as shit, 5 minutes in it clicks after the video i know it like the back of my hand. Love it!
@Skus0 Жыл бұрын
I wanna cry from the moment of understanding and clarity this video gave me after spending hours trying to understand induction from my discrete math textbook
@eugenepark80586 жыл бұрын
Dude. This video is about 7 years old but IT IS GOLD!!!! Thank you so much!!
@afrojacker98 ай бұрын
12 years
@CilantroJo12 жыл бұрын
You explained this better in 9 and a half minutes than my teacher did in 3 days. Mr. Khan, i love u bro.
@jasmynedaniels570010 ай бұрын
I had an epiphany of understanding watching this, this was really helpful!
@Tee03133 ай бұрын
You've made it so easy
@strawberrytofu5174 Жыл бұрын
I am so lost in my discrete math course but I think I’m finally understanding thanks to this video, thank you so much
@deladonics11 жыл бұрын
Thank you for this. I love you very much.
@johns.822010 жыл бұрын
My math course basically tries to regurgitate all of this in like half of one lesson- I really wish they did a full lesson on it. It's only slowing me down. This is a lot (a LOT) of help though.
@Rinzlov12 жыл бұрын
That was clearest possible way to teach that. Thanks a lot!
@celenial6009 Жыл бұрын
ngl this was still kind of confusing, but it really helped a huge bunch, even though this is just the math for it, without the actual proof structure. 🙏thx
@vladaman112 жыл бұрын
This is extremely useful in computer science and electrical engineering
@lenardfrancis868710 жыл бұрын
Definitely better than my school teacher... Now i understand it so well Thanx a lot khan :)
@alex64552 жыл бұрын
I just had the "oh my god it's clicking" moment that every student studying mathematics and science strives for. Thank you so much for this!
@mickycheese2712 жыл бұрын
You have to substitute K+1 for all values of 'n' so it will be K+1[(K+1)+1]/2 = K+1(K+2)/2 Reason for doing this is because 'n' represents all positive integers. The reason why you can't substitute 'n' in place of 'k' is because 'n' represents any positive integer while 'k' represents a specific unknown integer. when one is added to 'k' then a new integer is formed 'k+1'. Therefore K+1 = n when P(K+1) is a function for n.
@therealjordiano13 жыл бұрын
11k views and no dislikes, a testament to your greatness khan :) fantastic tutorial ... this looks extremely tricky to learn from a text book o_o
@TimoKvapil2 жыл бұрын
watching this 10 years after you, with 1 million views. the impact that one 9 minute video has had is crazy
@seyranshafie4 ай бұрын
really helped thanks
@vannotan1737 Жыл бұрын
OMG Nice explaination !
@savanah27048 жыл бұрын
As a sophomore in a college algebra class this is a godsend.
@ninjapirate1234 ай бұрын
how's life now
@TheLodii12 жыл бұрын
You're saving the lives of everyone stuck with terrible professors! Thank you!
@ninjapirate1234 ай бұрын
hows life now
@treyatl200612 жыл бұрын
The binomial formula is just (x+y)^m = SUM k=0 to m; mCk*x^m*y^k. I'm not 100% sure about this but you must get it into the binomial coefficient form by letting x=n and y=0 using the binomial formula. Therefore, n^2 implies (n+0)^2 = 2C0*n^2*0^0 + 2C1*n^1*0^1 + 2C2*n^0*0^2. Hopefully this help some...
@ruidechen9 жыл бұрын
Thanks! Really helped me. My prof has a heavy accent so I have a hard time trying to make sense of what he said when he went through this. Now I know perfectly how this works! :)
@madhur75908 жыл бұрын
Khan academy is the best Salman Khan is doing really good thing by providing free education online for everyone
@ruba.-.3716 Жыл бұрын
I was first grade when he uploaded this video n now I’m in my first year college watching his videos 🤭
@alialdinmohamad100011 ай бұрын
Love your content. amazing job my mam. keep up the good work!
@wideawakeanimal110 жыл бұрын
That very last step, fucked my mind up man! :(
@g.guevarra8 жыл бұрын
Thanks a lot really helped me with pre calculus!
@mbrochh8211 ай бұрын
This is amazing.
@nickkapiskis88726 жыл бұрын
Thank you so much, everything is so clear now!
@DashingAsianGuy12 жыл бұрын
we have an exam for tomorrow I know step 1 but the 2nd step induction is to hard for me and I've been diligently listening to my prof all the time. I wish there's a way for me to ace this subject and completely understand it. your video is informative though. it's getting a bit clearer now.
@knightspygaming1287 Жыл бұрын
How did you get the formula of n(n+1) /2 , Cuz in my exam formula wasn't given. Is it question?
@rajatchhabra35415 жыл бұрын
You did not mention why we should use 'proof by induction' in the first place? In which situations can we use this?
@murphy38075 жыл бұрын
Statistics. It's how they get a standard number for probability or a constant number for algorithms.
@justjesslyon12 жыл бұрын
I FINALLY understand. I should just watch your videos rather than go to my math lectures.
@yost2812 жыл бұрын
Way better than my professor at the university. Honestly questions the value of higher education. Anyways thanks for this. Definitely the hardest concept in my discrete math course.
@dakotagagne88405 жыл бұрын
Very helpful. Made way more sense than my lectures
@merlinthegreat1009 жыл бұрын
Khan academy pre-calc lectures + a pre-calc textbook = yet another grade of math that I will skip
@cyanmatrix72694 жыл бұрын
thank you khan academy for teaching me more than my prof's
@Marius-vw9hp6 жыл бұрын
"true for two, true for three, true for four". Now THATS a tongue twister.
@cary_domiii5 жыл бұрын
I'm now a 2nd Year Secondary Education Student Major in Mathematics and it is only by now that I've understood this topic well....
@hellokat6811 жыл бұрын
please add correct English subtitle to your videos, it's helpful for non-native english speakers like me, thanks
@mtado4933 Жыл бұрын
man, 2 hours with my math teacher, thanks for the help!
@sallaklamhayyen98762 жыл бұрын
Hi, Khan thank you so much and please do a discrete math course
@pokemonnarutodbz110 жыл бұрын
thank you very much. this has helped me quite a lot. I don't really have a good mathematics teacher, so I rely on this channel for tests.
@RazaAshai8 жыл бұрын
Please do a video on strong induction
@edwardm72928 жыл бұрын
THISSSSSSSSSSS
@RealEverythingComputers27 күн бұрын
Thanks for the great video!
@majdalkwaja97922 жыл бұрын
thx , this is how it is supposed to be explained
@AalejandroI13 жыл бұрын
Thank you, I had been looking for a vid on mathematical induction for quite a while :)
@ElenaSemanova6 жыл бұрын
This genuinely makes me happy.
@mickycheese2712 жыл бұрын
he took the common denominator '2'. Reason: When taking common denominator for (K+1), he has to multiply '2' to the numerator too so the equation stays balanced. If he didn't do that then the previous step would not be equal to the current step. All he did was added fractions with unequal denominators.
@ermi14433 жыл бұрын
Excellent video👏🏾
@SynchronizedProgramming4 жыл бұрын
Wow thanks I see a lot of people use n and n-1 for the induction proof
@bradleymorgan82233 жыл бұрын
No matter how many math courses i've taken through the years, this man has always been there. I owe you a debt of immense gratitude!
@WilliamFordRoom34010 жыл бұрын
It has been years since I have had to work on proofs. This makes it much easier to keep up my college math skills. Thanks!
@johnholme7836 жыл бұрын
Thanks for taking the time to produce these videos. You have a talent for teaching mathematics and physics for the layman. Thanks to these videos I now have a good intuitive understanding of numerous mathematical and physics concepts. Keep up the good work.
@ahnafsamin10 жыл бұрын
Finally I have understood the concept.Thank you Khan!
@MinnesotaFarmboy9 жыл бұрын
I was able to follow the explanation until index 7:45, at which point I found it very confusing. Some things are written in yellow, and it is stated that, "well we have just proven it," ("it" is an unclear object in this case). I realized that the problem was that you haven't related "it" to the original premise by showing that every instance of k in the S(k) formula (written in green) had been replaced by K+1 at the end (written in yellow). It appears that you got excited when you got close to the end and forgot to relate it to S(k) or to show it graphically by drawing a line between them.
@fikretcihan1747 Жыл бұрын
Congratulations. Notification: I would like to inform you that I plan to include this video among the videos reviewed in my article "Analysis of KZbinTM Videos and Video Comments on Mathematical Proof Methods". Kind regards.
@ASLUHLUHC36 жыл бұрын
OMG YOU SOMEHOW MADE IT CLICK FOR ME YOU ABSOLUTE LEGEND
@omerbahat540810 жыл бұрын
Thx helped me study for my test
@AssAssinAddiction4 жыл бұрын
ive been watching so many videos trying to understand induction for my discrete maths class and this just broke it down so nicely for me. Thank you so much for this video.
@lb677010 жыл бұрын
kahn has once again saved my life (and by life I mean my test grade)
@KeshavKhanna10 жыл бұрын
Its Khan.. If someone saves your life.. spell their name right :)
@jff7112 жыл бұрын
Thank you very much!
@johnparker109011 жыл бұрын
Good explanation, I totally got it. Thanks
@Bkaz36787 жыл бұрын
God help me, I still don't get it.
@rahilarshad24565 жыл бұрын
kzbin.info/www/bejne/mn7RZqpqlN-nidk
@aggelosspirou88155 жыл бұрын
i dont know if u ever will see this but i hope this helps Prove that Σn= n(n+1)/2 for every possible integer n step 1 : know that something is true about Σ(1) . In our case it's Σ(1)=1(1+1)/2=1 step 2 :assume that Σ(k)=k(k+1)/2 is true step 3: since Σk=k(k+1)/2 based on step 2 we can now prove that Σ(k+1) = (k+1)(k+2)/2 explanation : Σ(κ+1) = 1+2+...+κ+(κ+1)= Σκ + κ+1 = (κ(κ+1)/2) +κ+1 ( based on step 2 )=κ(κ+1) + 2(κ+1)/2 = (κ+1)(κ+2)/2 . which is what we were looking for. But since S(n)=n(n+1)/2 is unquestionably true for S(1) ,we proved that it's true for S(2) aswell.And since now this is true for S(2) according to our proof it should be true for S(3) aswell. and it goes. hope this helped and ask anything if u want
@j0shda1164 жыл бұрын
@@aggelosspirou8815 oof what the hell did you write
@saranamuli91344 жыл бұрын
thank you so much i have finally understood it but my question is whats the point? whats the point of proving by induction? why do we do it? why do we use it? i prefer to understand something than take it as it is so if anyone can answer me ... thank you
@henri1_964 жыл бұрын
@@saranamuli9134 Even if we have no idea why a statement is true, we can still prove it by induction.
@fathimareeza15556 жыл бұрын
Why do we have to add the (k+1) in to the left side of the equation? Also do have to add that (k+1) in to the left side of the equation whenever we want to prove induction?
@pompouspineapple76223 жыл бұрын
THANK YOU SO MUCH YOU SAVED ME THANK YOU
@renillasubero26628 жыл бұрын
Oh my I finally understand this clearly !!
@RtsFps1 Жыл бұрын
When I distribute the K and the 2 to their respective (k+1) I get the same thing on both sides which is good. But I don’t understand how to factor out the two Ks to get it to look like (k+1)(k+2).
@mosweutumelo88molfh13 жыл бұрын
much better than my lecturer
@cp3foreverever13 жыл бұрын
lovely video, the pretty colours were very helpful
@rhoadess13 жыл бұрын
I like the Alternative proof better, it is more intuitive.
@Aevatheone7 жыл бұрын
Thank you for making this available and thank you so much for actually explaining each step from 0 to 1.