That's because modern mathematicians closed the door behind them. They get to learn from G polya, Rudin, and Abbot. And we get squat, they want mathematics to be exclusive. Read the old masters. They cared more for their students.
I am a project manager and work at a company. I spend my free time with Khan videos when I need relaxation, I sometimes watch before getting on a plane, sometimes at my breakfast table, sometimes prior to sleep. These videos help me remember all those calculus equations and theorems from my university life. It's like seeing old photos with my friends. I prefer Salman Khan over funny cat videos :)
I wish we had teachers like you at my college. I never understood this concept and i always ran away from it. But today i totally understood everything just because of your explanation. Thanks a lot for making such a cool site and that too for free! Students like us will always appreciate you for making our studies so much more fun with your cool videos and site. :)
Currently taking calc analysis as a com sci major, and this video has proven INVALUABLE, watching it in 2017 8 years after it was made and it's literally doubled my understanding of limits
Thank you so much for all of your videos. I read and re-read my textbook and reviewed lectures for HOURS on end and still couldn't make heads or tails of the course material. Then I watched a few ten-minute clips from your channel and completely understood what I was doing and how to complete my assignments. Thanks to your videos, I just got 100% on my first quiz. By the way, I haven't taken a math course in 16 years, and was just thrust into Calculus. Another testament to how good these videos are!
I'm taking a Calculus 1 class at a local city college. My professor is discussing how to prove limits using epsilon and delta. Very confusing. But after watching your video you make it look like child's play. Keep up the good work!
Thanks for the video =) it would be really awesome if you uploaded more videos of epsilon delta proofs of limits of more complicated functions (of one and two variables). I'm sure I'm not the only one who would appreciate that very much!
Whenever this came up in lectures and worksheets, I always found myself only getting a vague idea of what was actually going on, even after reading through many times and getting help from my tutor. But these two videos have succeeded in connecting all the dots and now everything makes perfect sense! Thanks for providing such a useful resource!! :)
I'm rewatching to rehash what I already picked up. In the last video, he explained epsilon in a way it made the absolute values of the definition understandable and it clicked. So nice having this guy
I study maths at a fairly prestigious university, but still, I understand this so much more now than I do reading my stupid textbook and being at unimaginably complicated lectures. So much better to just do education (at least first or for review) through khan academy so maths isn't so hieroglyphic all the time... :)
thank you! I love how you can explain it in less than 30 minutes and my professor gets paid to stand there pointing at the definition for about 2 hours mocking students and making excuses.
My math professor tried to teach this to us the second day in a beginner calculus class… I really am praying for those that haven’t done calculus before 😭
I've been trying to understand this for a long time, I've searched a lot in the web and I must say this is the clearest explanation I've found. It's awesomely clear!!!!!!!! Thank you very very much!!!!!
really.. THANK YOU!! for explain it as clear as you did and make me finally understand the epsilon-delta definition.. i've been just running in circles with this definition untill i found this, it seems you are one of the few people in this world who are able to make it easy to see xD
Glad to hear I'm not the only one. I'm a joint honours physics and math and my physics prof used this limit definition in the definition of phase spaces, so I've decided I'd finally go back and make sure I understand this well.
I just started my actuarial science course and we were learning bout the epsilon-delta definition for nearly 2 hours. I couldn't really register what the lecturer was trying to convey. But damn Sal conveys it in 10:56. He sure has magic. \m/
THANK YOU! I have an exam that involves this on frdiay, and I was absolutely lost until I watched this video. I will be coming back to you for future calc problems I have.
I don't comment on videos like these but I have to, you took a topic I've been struggling with for days and made me understand it so well. I love you homie.
sal i have a question: At 3:30 why haven't you stated that [3x(x-1)/x-1] -3 also NEEDS to be bigger than zero because if it does equal to zero that means that in the given function at 3 on the y-axis there is a point that exists. HOWEVER at 3 on the y-axis there shouldn't be any point in existence because if x cannot be equal to 1 y cannot be equal to 3, unless you've defined that there is a point on the y-axis at 3 but not when x=1 (which you haven't done)
In the very beginning, he stated that epsilon has to be greater than zero. Thus, since epsilon is already defined to be greater than zero, there is no reason to restate it. You may then ask, however, why did Sal then include that for the delta inequality when it was also already defined to be greater than zero, but not for epsilon (which in fact is the case in my textbook as well as Wikipedia and many other sources, which leads me to think it is intentional)? This is because we want to force the absolute value statemen in the delta inequaly to be greater than zero as well. This is because the absolute value could result to zero, and still hold with delta being greater than zero, but we also want the absolute value statement of x-1 to be greater than zero, so that the value x never actually equals what its approaching. Hope this helps! :)
It's so simple to apply once you actually know wtf it means. It's just a restating of something you already have somewhere in your head if you know what a limit is. That point is made here way better than in a textbook, the continuity and logic is really shown where before you would have to figure that out yourself.
Well the ridiculously fast pace of first year math means profs don't fully explain the fundamentals of ideas in class. Slower pace is definitely needed to absorb and reflect on new ideas learned. Horray for khanacademy!!!
it took me a whole day to understand my teacher lecture but still could not understand. Then i headed to University of RUclips and i got Sal. Thanks for saving us!
It took me watching this video three times with solving and pausing and thinking, to hopefully fully understand the concept, and its really okay if you can't get the full picture in the first go.
even though it was a one variable function, this lecture helped me understand the two variable epsilon delta limits too... awesome explaination. thanks @khanacademy
wonderful work. you manage to be precise without being overwhelming and the moderated length (measured in t dimension) of the videos is highly pedagogical.
Back in the days this was the only thing I could not understand in my math course. Now that I watched this I think it was because then I had bad teacher
English is not my native language and I don't speak or even understand so well and It's incredible that I have understand more with this explanation than with spanish explanations, besides in part could be 'cause there are only two or three videos that explain that maked by students.
Yes!! Thank u sooo much! for some reason noone else explained the logic of these problems they only told how to do it. So thanks soo much for explaining! Plus i love the tech u are using. This video was EXACTLY what i was looking for! Im gonna get A's beatch!
omg thank you so much for explaining this in a concise and understandable way!! my professor tries to make everything way more complicated than he needs to... I think he always tries to get the lowest test average because he brags about that -_-
man, i miss the times when they taught logic in school... if, then, if and only if, all this is explained in logic, and students could tie the two objects so well with each other...
I'm in the best math university in my country and nobody can explain it as good as you. Thanks!
Which country and university?
IIT XD
this guy is graduated from MIT holding 2 bachelors and 1 master degree at the age of 22 dude
MSU(Moscow State University)? Or in russian МГУ?
That's because modern mathematicians closed the door behind them. They get to learn from G polya, Rudin, and Abbot. And we get squat, they want mathematics to be exclusive. Read the old masters. They cared more for their students.
I am a project manager and work at a company.
I spend my free time with Khan videos when I need relaxation, I sometimes watch before getting on a plane, sometimes at my breakfast table, sometimes prior to sleep.
These videos help me remember all those calculus equations and theorems from my university life. It's like seeing old photos with my friends. I prefer Salman Khan over funny cat videos :)
lol
lol learning and cat videos are not mutually exclusive.
ye melata lij ashkabatch
i like to learn those things i didn't have the motivation to learn while i was lazing around at university lol
I wish we had teachers like you at my college. I never understood this concept and i always ran away from it. But today i totally understood everything just because of your explanation. Thanks a lot for making such a cool site and that too for free! Students like us will always appreciate you for making our studies so much more fun with your cool videos and site. :)
Currently taking calc analysis as a com sci major, and this video has proven INVALUABLE, watching it in 2017 8 years after it was made and it's literally doubled my understanding of limits
2017 being 7 years ago is crazyyyyyy
Thank you for the awesome video, Sal. Never forget how many students you are helping!
true that!
Thank you so much for all of your videos. I read and re-read my textbook and reviewed lectures for HOURS on end and still couldn't make heads or tails of the course material. Then I watched a few ten-minute clips from your channel and completely understood what I was doing and how to complete my assignments. Thanks to your videos, I just got 100% on my first quiz.
By the way, I haven't taken a math course in 16 years, and was just thrust into Calculus. Another testament to how good these videos are!
You know something is tough even if a great teacher teaches and you still don't understand
Had to watch it a few times before getting it
@@inversechaos9256phew....I'm not alone.
I'm taking a Calculus 1 class at a local city college. My professor is discussing how to prove limits using epsilon and delta. Very confusing. But after watching your video you make it look like child's play. Keep up the good work!
Thanks for the video =) it would be really awesome if you uploaded more videos of epsilon delta proofs of limits of more complicated functions (of one and two variables). I'm sure I'm not the only one who would appreciate that very much!
You made this much easier to understand than my college professor.. great job!
Whenever this came up in lectures and worksheets, I always found myself only getting a vague idea of what was actually going on, even after reading through many times and getting help from my tutor. But these two videos have succeeded in connecting all the dots and now everything makes perfect sense! Thanks for providing such a useful resource!! :)
This man is 100% responsible for my education!!! We appreciate you Sal Khan
I'm rewatching to rehash what I already picked up. In the last video, he explained epsilon in a way it made the absolute values of the definition understandable and it clicked. So nice having this guy
The video is almost 11 years and still very helpful. That's the beauty of math, the rules never change.
haha I love it!
"IFFFFFFFFFF..."
I study maths at a fairly prestigious university, but still, I understand this so much more now than I do reading my stupid textbook and being at unimaginably complicated lectures. So much better to just do education (at least first or for review) through khan academy so maths isn't so hieroglyphic all the time... :)
thank you! I love how you can explain it in less than 30 minutes and my professor gets paid to stand there pointing at the definition for about 2 hours mocking students and making excuses.
Sweet, read this over and over but still was never very clear on this definition. Your plain 'n simple, visual/audio method is awesome man.
My math professor tried to teach this to us the second day in a beginner calculus class… I really am praying for those that haven’t done calculus before 😭
Oh man..what kind of calculus is this..i havent seen this in my whole life..how intelligent was the inventor of this was that..!!!
I've been trying to understand this for a long time, I've searched a lot in the web and I must say this is the clearest explanation I've found. It's awesomely clear!!!!!!!!
Thank you very very much!!!!!
You made this video when I was in 1st grade, 12 years later I'm watching this and its helping me so much more than my professor or TA.
really.. THANK YOU!! for explain it as clear as you did and make me finally understand the epsilon-delta definition.. i've been just running in circles with this definition untill i found this, it seems you are one of the few people in this world who are able to make it easy to see xD
Hello are you there?
I just spent two days trying to figure this out.... and you had me an expert at it in under an hour. Thank you so much!
Very intuitive. Surprisingly clear. Thanks for taking the time to explain topics like these Sal!
You are the "Lionel Messi" of Education
José Saavedra Cristiano Ronaldo*
Khan is the best, so Messi is the one you want to compare him to.
Glad to hear I'm not the only one. I'm a joint honours physics and math and my physics prof used this limit definition in the definition of phase spaces, so I've decided I'd finally go back and make sure I understand this well.
I just started my actuarial science course and we were learning bout the epsilon-delta definition for nearly 2 hours. I couldn't really register what the lecturer was trying to convey. But damn Sal conveys it in 10:56. He sure has magic. \m/
Oh, God! Finally I understood the definition of limits! Thank you Khan :)
Oh my God, I seriously just.... love you.
You are my favorite person right now, you're just.... incredible.
Stay God-like
I FINALLY UNDERSTAND!!!! this is like the 5th video I've watched
THANK YOU! I have an exam that involves this on frdiay, and I was absolutely lost until I watched this video. I will be coming back to you for future calc problems I have.
Hello are you there?
I don't comment on videos like these but I have to, you took a topic I've been struggling with for days and made me understand it so well. I love you homie.
omg i love you. after watching everything and anything i understood what i actually have to do. thank you so much !
Sal remains the best video instructor i have seen so far. Correct me if I am right.
Had been trying to understand this for a week and I was stressing out!! And boom it just clicked! I’m so happy, thanks!
sal i have a question:
At 3:30 why haven't you stated that [3x(x-1)/x-1] -3 also NEEDS to be bigger than zero because if it does equal to zero that means that in the given function at 3 on the y-axis there is a point that exists. HOWEVER
at 3 on the y-axis there shouldn't be any point in existence because if x cannot be equal to 1 y cannot be equal to 3, unless you've defined that there is a point on the y-axis at 3 but not when x=1 (which you haven't done)
In the very beginning, he stated that epsilon has to be greater than zero. Thus, since epsilon is already defined to be greater than zero, there is no reason to restate it. You may then ask, however, why did Sal then include that for the delta inequality when it was also already defined to be greater than zero, but not for epsilon (which in fact is the case in my textbook as well as Wikipedia and many other sources, which leads me to think it is intentional)? This is because we want to force the absolute value statemen in the delta inequaly to be greater than zero as well. This is because the absolute value could result to zero, and still hold with delta being greater than zero, but we also want the absolute value statement of x-1 to be greater than zero, so that the value x never actually equals what its approaching. Hope this helps! :)
Oh my god!! I have been struggling to understand this definition of limit. And your video cleared it in seconds. Thank you so much man.
It's so simple to apply once you actually know wtf it means. It's just a restating of something you already have somewhere in your head if you know what a limit is. That point is made here way better than in a textbook, the continuity and logic is really shown where before you would have to figure that out yourself.
Praise our lord and saviour Khan!
You almost had me with the first video, but by half way through the second...you had blown my mind. I am going to have to watch this again.
OH MY GOD!Thank You!!
I finally understand this! I have a final tomorrow and now I'm a lot more confident!!
thank youu!!! :D
I don't know what my education would've been like without Kahn.
Well the ridiculously fast pace of first year math means profs don't fully explain the fundamentals of ideas in class. Slower pace is definitely needed to absorb and reflect on new ideas learned. Horray for khanacademy!!!
Alright! Once I find a couple of practice problems to test drive this concept on, I think I'll be set. Thanks!
this guy is a BEASTTTTTT
thank you so much you are my new calculus teacher
Thanks Sal. I generally don't have trouble with Calc, but the notation for these proofs confused me utterly. This makes much more sense.
This is seriously better than Caltech Ma1a lectures.
it took me a whole day to understand my teacher lecture but still could not understand. Then i headed to University of RUclips and i got Sal. Thanks for saving us!
It took me watching this video three times with solving and pausing and thinking, to hopefully fully understand the concept, and its really okay if you can't get the full picture in the first go.
I have never really understood epsilon delta proofs until now. Great video!
You are a math hero. Thanks for the help!
I'm a very visual learner. This was brilliant.
YOU ARE A LIFE SAVER!! THANKSSSSS
These lectures are gold mine for us. Heartiest Thanks to Khan Academy team.
You deserve all my college money cause you care to teach more than my professors do
Thank you SO much!! You made me understand this way better than my teacher did during three lectures IN MY OWN LANGUAGE!!
Thanku very much sir....it clears my concept upto 90 percent..
I am in a IIT and still watching a 11 year old Khan academy video...
Thank you so much, youre the reason i'll pass calc
OMG exam tomorrow and you saved my life! thank you :)
Watched many videoes on the same topic but understood the concept by this.
wow. thank you. i really hate these proofs.. but i think i understand it a bit better. i'm sure a second time watching this and i'll be good to go!
i got 35% in my calculus class test... wish i watched this earlier! thanks so much though, hopefully will do better in my exam in jan :) x
This is is better than the updated video you guys have
Finished watching this now - brilliant video.
Oh my god it makes perfect sense now and I can even visualise this stuff... Awesome video.
That moment when it FINALLY made sense. So good. Ty
I never understand anything until Khan academy explains it to me.
hip hip hurray! For he's a jolly good fellow, which nobody can deny!
I wish I had the internet when I was in college!
even though it was a one variable function, this lecture helped me understand the two variable epsilon delta limits too... awesome explaination. thanks @khanacademy
Beautiful explaination ! ....Thank you .
This is better than a textbook!
that's usually the case. the epsilon side can usually be simplified to be the delta value so that the final value will be the delta
wonderful work. you manage to be precise without being overwhelming and the moderated length (measured in t dimension) of the videos is highly pedagogical.
Can't believe this is in Calc 1 for me but that's okay. I feel like I can learn everything from you!
Awesome. Love the notation. Thanks Sal!
Thank you Mr. Khan for teaching the entire concept of limits
Thank you! save me from elementary real analysis!
Back in the days this was the only thing I could not understand in my math course. Now that I watched this I think it was because then I had bad teacher
All of a sudden everything makes sense. THANK YOU.
Man I am glad I looked this up in my 3rd week of freshman year
I'm sure you get this 1,000 times a day, but you definitely just saved my Calculus test grade.
very good example quite helpful, isn't it sad that university professors that get paid money to teach can't explain it as well
Not everyone's a genius like you.
Finally this actually makes sense
Really good explanation...
I thank u for such video u uploaded.
once again thank you Khan academy !!!!!!
Really thankful for this video specially I really couldn't get this concept till on even though i tried
You really make great instructional vids. thankyou.
And quick ...or at my own pace..
Love from Malaysia.
I finally understand!!! U hve been my biggest help ever!!
English is not my native language and I don't speak or even understand so well and It's incredible that I have understand more with this explanation than with spanish explanations, besides in part could be 'cause there are only two or three videos that explain that maked by students.
The best University of the world.
I will donate you when I will earn money.
But you need to wait for at least 5 years
Oh man fantastic video. This helps a bloody ton.
Yes!! Thank u sooo much! for some reason noone else explained the logic of these problems they only told how to do it. So thanks soo much for explaining! Plus i love the tech u are using. This video was EXACTLY what i was looking for! Im gonna get A's beatch!
Any one like who is here after 14 years
omg thank you so much for explaining this in a concise and understandable way!!
my professor tries to make everything way more complicated than he needs to...
I think he always tries to get the lowest test average because he brags about that -_-
man, i miss the times when they taught logic in school... if, then, if and only if, all this is explained in logic, and students could tie the two objects so well with each other...
9:00 WHOA... I got it! I understand the circular proof as not circular!!!