This is a common line you've heard millions of times, but i wanna say the line: Thank You. I've not seen any simpler explanation of Epsilon-delta than this one and I'm not confused anymore. A Big Thank You and Congratulations!
I learned this yesterday in class and the teacher lost me as soon as he said Epsilon/Delta. This was a fantastic explanation which I understood completely. Thanks!
omg i watched about 5 videos to try to understand this definition and it finally clicked completely after watching yours! you explained this so well!! thank you so muuuuch!
Yours is the best explanation of this I have thus far found, as I keep looking trying to understand. (Fortunately I am long out of college and am doing this just for fun, for certain definitions of "fun"). Here's what I've managed to mash into my brain: - A limit for a given y value exists at a given x value, if you can say that, as you get closer and closer to that y value, you also get closer and closer to that x value. That's intuitive from a human brain perspective; the trick is to express that with mathematical rigor and precision. - A good way to do "epsilon implies delta" is to find a function that relates the two. It's not strictly required, but it's the simplest way to prove all values of epsilon and delta, and it works well for non-pathological functions, so let's try to do that. If you can demonstrate the relationship, then you've got a couple of nested inequalities: epsilon is the outer bound of whatever relationship you've set up with delta, which in turn is the outer bound of how far you're straying from your target x. - The epsilon / delta thing can break if you're trying to be jerk about it, but limits assume you're not trying to be a jerk. Like if you were trying to do the limit of sin(x) as x approaches 0, if you try to set up your delta and epsilon and say "a-HA! but it doesn't work if you evaluate epsilon and delta at x = 23 pi", no, that's just you being a jerk. When you're near x = 0, it works fine. As in all things, don't be a jerk. Sooo. I'm trying to prove the existence the limit of sin(x) as x approaches 0. What I end up with is that epsilon > |sin(delta)| ; is that a correct result? I THINK I have demonstrated a relationship between epsilon and delta, which means that any little distance I stray from x = 0 (less than an arbitrary delta) will mean that my function will stray from sin(0) by less than epsilon (which equals |sin(delta)| ). I can make delta crazy small, which means epsilon can get crazy small too, which means that I can get epsilon down to effectively zero (though not exactly zero). And that's the limit.
Thanks a million! I remember this class, and I remember being extremely confused. I just did my homework in about 15 minutes for this section after watching this video. Absolutely amazing
Krista, as I’ve said time and time again, you are brilliant, a great, great teacher, and a wonderfully nice person, all simultaneously. You hit the Trifecta. Hardly anyone can do that. You’re the best. ☺️❤️👏👍
I just started Calculus this semester and honestly, this section really confused me more than I was expecting. Thanks so much for clearing this up, incredibly helpful!
Hello I don't understand why, at the end of the video, you made delta less than epsilon? I understood that both delta and epsilion's inequality have the same value ( x+3), but how does that make it possible to make one less than the other? Also in some videos they make delta = to epsilon?
If you choose delta bigger than epsilon, then that would basically mean that delta could be however big, but that would make no sense since you want delta that gives an interval of x-values that still gives (x) a value between (L + epsilon) and (L - epsilon). Remember that delta depends on what epsilon you choose and not vice versa. Delta is limited by the chosen epsilon (as long as the chosen epsilon is bigger than zero).
@@namihiko8678 No idea actually, but I haven't studied math in a while so I'm not sure :) Spontaneously I would guess that maybe for some problems epsilon=delta can be one solution that proves the limit, but that this isn't always true. But please don't take my word for it, I haven't studied math in a while.
@@namihiko8678 Delta depends on what epsilon you choose, and if I remember correctly there are many different deltas that you can choose that falls within the interval that still gives a value that is close enough to the limit (within an epsilon of distance from the limit). Sometimes putting delta=epsilon is one correct solution I guess.
Six years later and still no answer to your very valid question. Well, except by Nora Sverredal who by her own admission has "no idea" what the answer is and hasn't "studied math in a while" but is still willing to "explain" (i.e. guess).
Hi Krista! I am Great IT Courses on Udemy (Raschedian). I have a couple of mathematics courses on Udemy. You teach mathematics very fluently! Great job!
You could pick a value larger than 5, but only barely, and you could not pick 7. The value you pick needs to be inside the interval for delta, which ends on the right at about 5.5. As long as you keep it within that, you're good.
Lol I can't stand Khan. The background and writing was similar. You have good stuff. I'll definitely be checking more out. I'm sure you're getting this a lot but thank you for making these videos. It helps so many people. Every good channel out there is like a goldmine to those who are looking. Cheers!
Sorry but very unlike your typical videos (which I recall liking a lot), this talk on limits is just terrible. The limit is just dX = 1/n where n is an indefinitely large number. Sometimes other terms are used like h etc. But dX was devised by the co-founder of calculus Liebnitz and there is no good reason to use other terms. Classically the limit is taken on the reference axis which is usually the X axis. The corresponding value on the Y axis is dY. This may equal or be greater or smaller than dX and the ratio dY/dX gives the tangent and its angle (direction). Note the d of X and d of Y are not necessarily equal and cannot be canceled out. Rest is all gobbledegook.
God this is such a pretentious and unnecessary complicated way to say "this random number is bigger than this other random number". Your explanation is great but I can't see how this gives a further understanding of limits.
OH MY GODDDD!!!!!!!!!!!! I barely ever comment on any video but I just couldn't leave this video without subscribing, liking, and leaving a comment to say THANK YOU SO MUCH!!!! Like the concept is extremely easy and logical but for some reason professors tend to overcomplicate it for absolutely no reason!! 🤍🤍🤍🤍🤍
You are literally the only person I found who bothered to explain what delta and apsilom actually was, thank you so much
You're welcome, Nicholas, I'm glad I could help! :)
What is delta and apsilon?
@@marrybatool Greek symbols
@@marrybatool you'll need to understand open neighbourhood for that
I know right 😂😂...you're a better teacher for it❤❤
Taking calculus in college, 1 hour video from my teacher is nothing compared to this, thanks!
You're welcome, Kainny, I'm so glad this helped! :D
This is a common line you've heard millions of times, but i wanna say the line: Thank You. I've not seen any simpler explanation of Epsilon-delta than this one and I'm not confused anymore. A Big Thank You and Congratulations!
Aw thanks! I'm so glad it could help. 😊
I learned this yesterday in class and the teacher lost me as soon as he said Epsilon/Delta. This was a fantastic explanation which I understood completely. Thanks!
+donnydorito You're welcome, I'm so glad it made sense!
omg i watched about 5 videos to try to understand this definition and it finally clicked completely after watching yours! you explained this so well!! thank you so muuuuch!
Oh good!! I'm so so glad it finally came together! :D
As a math tutor, I think I'll find this video helpful for helping students. Thanks for sharing!
Mravsfan06 You're welcome, I hope it'll be helpful!
this is the first video that i actually understood
I'm so glad it made sense! :D
I don't know you but I love you lol. You teach really well!!!
Your explanations are always so precise!
thank you so much literally no one else explained what epsilom and delta is. you have helped me a lot!
Yours is the best explanation of this I have thus far found, as I keep looking trying to understand. (Fortunately I am long out of college and am doing this just for fun, for certain definitions of "fun").
Here's what I've managed to mash into my brain:
- A limit for a given y value exists at a given x value, if you can say that, as you get closer and closer to that y value, you also get closer and closer to that x value. That's intuitive from a human brain perspective; the trick is to express that with mathematical rigor and precision.
- A good way to do "epsilon implies delta" is to find a function that relates the two. It's not strictly required, but it's the simplest way to prove all values of epsilon and delta, and it works well for non-pathological functions, so let's try to do that. If you can demonstrate the relationship, then you've got a couple of nested inequalities: epsilon is the outer bound of whatever relationship you've set up with delta, which in turn is the outer bound of how far you're straying from your target x.
- The epsilon / delta thing can break if you're trying to be jerk about it, but limits assume you're not trying to be a jerk. Like if you were trying to do the limit of sin(x) as x approaches 0, if you try to set up your delta and epsilon and say "a-HA! but it doesn't work if you evaluate epsilon and delta at x = 23 pi", no, that's just you being a jerk. When you're near x = 0, it works fine. As in all things, don't be a jerk.
Sooo. I'm trying to prove the existence the limit of sin(x) as x approaches 0. What I end up with is that epsilon > |sin(delta)| ; is that a correct result? I THINK I have demonstrated a relationship between epsilon and delta, which means that any little distance I stray from x = 0 (less than an arbitrary delta) will mean that my function will stray from sin(0) by less than epsilon (which equals |sin(delta)| ). I can make delta crazy small, which means epsilon can get crazy small too, which means that I can get epsilon down to effectively zero (though not exactly zero). And that's the limit.
Thanks a million! I remember this class, and I remember being extremely confused. I just did my homework in about 15 minutes for this section after watching this video. Absolutely amazing
Krista, as I’ve said time and time again, you are brilliant, a great, great teacher, and a wonderfully nice person, all simultaneously. You hit the Trifecta. Hardly anyone can do that. You’re the best. ☺️❤️👏👍
I was having a hard time with calculus until I found your videos. I owe you so much and I have to Thank you.
You are so welcome, I'm so glad that I'm able to help!! :D
Never taken a Calculus class in my life....great explanation. Thanks for sharing.
I just started Calculus this semester and honestly, this section really confused me more than I was expecting. Thanks so much for clearing this up, incredibly helpful!
Thanks ten million times for this explanation , I was looking in the internet for days , you are amazing in the way you convey the lesson .
Well why didn't you just come to this video in the first place then? Just kidding. :)
Krista is the KING
You are best krista king I passed all many mathematics modules through yr tutorials
I'm glad I clicked on this video it made so much more sense with the explanations! Thank you so much!
This was so helpful, THANK YOU!!!
You're welcome, Jillian, I'm so glad it helped! :)
That was a marvelous explanation of the epsilon Delta definition
dpmike32819 Thank you so much!
I see you have upgraded your software for your presentations
U just saved me. Cant even explain how confused i was after this was covered in my lecture. THANK YOU
aced the first quiz of the year because of you, thank you
I'm so glad to hear that, Lia! Great job!! :D
Hello I don't understand why, at the end of the video, you made delta less than epsilon? I understood that both delta and epsilion's inequality have the same value ( x+3), but how does that make it possible to make one less than the other? Also in some videos they make delta = to epsilon?
If you choose delta bigger than epsilon, then that would basically mean that delta could be however big, but that would make no sense since you want delta that gives an interval of x-values that still gives (x) a value between (L + epsilon) and (L - epsilon). Remember that delta depends on what epsilon you choose and not vice versa. Delta is limited by the chosen epsilon (as long as the chosen epsilon is bigger than zero).
@@norasverredal1941 why do some books use "=" then
@@namihiko8678 No idea actually, but I haven't studied math in a while so I'm not sure :) Spontaneously I would guess that maybe for some problems epsilon=delta can be one solution that proves the limit, but that this isn't always true. But please don't take my word for it, I haven't studied math in a while.
@@namihiko8678 Delta depends on what epsilon you choose, and if I remember correctly there are many different deltas that you can choose that falls within the interval that still gives a value that is close enough to the limit (within an epsilon of distance from the limit). Sometimes putting delta=epsilon is one correct solution I guess.
Six years later and still no answer to your very valid question. Well, except by Nora Sverredal who by her own admission has "no idea" what the answer is and hasn't "studied math in a while" but is still willing to "explain" (i.e. guess).
i know this was posted a long time ago but thank you so much!! life saver
You are ammmmmaaazzing
✨✨✨✨✨✨✨
I was searching for understandable idea of that wierd definition
Great video. Missed math class today but your video helped me grasp the concept reasonably well.
Thanks Ushiki, I'm so glad it helped! :)
I wish I had found this video two days ago, it would've saved me two days of frustration trying to understand this haha.
this was the absoult amazing explaintion ...i'm emberesd!!
I needed this video, I'm glad i found it! Great work! It finally makes sense now!
I'm glad you found it too! Glad it could help. :)
I really love this way of explaining this definition
Thank you so much, Anshuman, I'm glad you liked it! :)
@@kristakingmath :)
Very thorough and clear, thanks!
***** You're welcome!
THANK YOU SO MUCH omg this was a fantastic explaination
a helpful video for sure! sounds like you have a sleeping roommate that you're trying to not wake up when you're talking though haha
Great content, I understood. Thank you😊
It really helped me, Thankks
You're welcome, James! :D
Best explanation of this concept in all of youtube.
Absolutely brilliant
nice explanation,
my math lecturer made it looked very hard
Glad it helped! 🤗
It was wonder full made it easy to understand, CRAZY
How did you combine the two inequalities? Can't it also be e/7 < (epsilon)?
so 7delta < epsilon would be the delta we choose for our proof ?
Hi Krista! I am Great IT Courses on Udemy (Raschedian). I have a couple of mathematics courses on Udemy. You teach mathematics very fluently! Great job!
You are a legend😊
at 6:08 can we pick value more than 5, let's say 7?
My professor has just started this section of Calculus and I am already screwed.
You could pick a value larger than 5, but only barely, and you could not pick 7. The value you pick needs to be inside the interval for delta, which ends on the right at about 5.5. As long as you keep it within that, you're good.
I got it. Videos are really helpful. You won my subscription.
Have a great Weekend!
I think that I finally get this. It's only confusing the first 100 times you read about it.
I wish you could be my calculus teacher
We have missed your smiley face !! :)
Is it possible that 0 < |x-a| < delta but f (x)=L ?
thanks so much!
+Brandon Moffett You're welcome!
can't the delta be less than or equal to the epsilon ??
perfect 👏🏻
Excellent.
Thanks, Emil! :)
Greatness 👏🌙
this made so much sense, my textbook did not lol thank you
You're welcome, Jocelyn, I'm so glad it helped! :D
awesome!!!!!!!!!!!!!!!!!!!!!
Thanks!! Glad you liked it! ❤️
@@kristakingmath I so did, your explanation of delta and epsilon RULES
Can anyone clarify delta and epsilon for me (ranges and boundaries)?
if i dont pull my socks this sem its over for me
You’ve got this!!! If there’s ever anything I can do to help, please reach out! ❤️
Almost skipped this video because I thought it was Khan Academy
I'm glad you didn't! I should probably change the thumbnail to make it easier. Hope it helped!
Lol I can't stand Khan. The background and writing was similar. You have good stuff. I'll definitely be checking more out. I'm sure you're getting this a lot but thank you for making these videos. It helps so many people. Every good channel out there is like a goldmine to those who are looking. Cheers!
Awww thanks! I'm so happy to be able to help! :)
@@kristakingmath You are god!
So confused lol
math god
I ain't lie - you got a cute voice
You ain't English either, apparently.
Sorry but very unlike your typical videos (which I recall liking a lot), this talk on limits is just terrible.
The limit is just dX = 1/n where n is an indefinitely large number. Sometimes other terms are used like h etc. But dX was devised by the co-founder of calculus Liebnitz and there is no good reason to use other terms. Classically the limit is taken on the reference axis which is usually the X axis.
The corresponding value on the Y axis is dY. This may equal or be greater or smaller than dX and the ratio dY/dX gives the tangent and its angle (direction).
Note the d of X and d of Y are not necessarily equal and cannot be canceled out.
Rest is all gobbledegook.
I actually find this video very helpful... if you don't like it then don't watch it! :)
Here's a newsflash for you, Nora: you HAVE to watch a video before you can know if you like it. Derp!
but how does this help us in life
God this is such a pretentious and unnecessary complicated way to say "this random number is bigger than this other random number". Your explanation is great but I can't see how this gives a further understanding of limits.
OH MY GODDDD!!!!!!!!!!!! I barely ever comment on any video but I just couldn't leave this video without subscribing, liking, and leaving a comment to say THANK YOU SO MUCH!!!! Like the concept is extremely easy and logical but for some reason professors tend to overcomplicate it for absolutely no reason!! 🤍🤍🤍🤍🤍