Precise Definition of a Limit - Understanding the Definition

[@MariamMansour-i7f]

This is literally a life saver. I had a 2 hour lecture that sounded like literal gibberish to me, and you beautifully explained it in a couple minutes.

[@R3nxt]

“You tell me how close you want to be on the y axis, and I tell you how close you need to be in the x axis. If that is possible, then we say the limit exists.”

[@jennylim02]

I absolutely do not understand why there are 12 dislikes, I mean you really changed my life. As an UCSD math student you helped me went through my lower math courses, can't believe that you are still here when I need help for my upper level math class, bless you with all my heart.

[@jehieljoseph1220]

Those dislikes are maths professors 😂

[@nikhilbalwani5556]

go*

[@-danR]

The dislikes likely have nothing to do whether he helped _you_ get through your courses, but from people who are still perplexed by the delta-epsilon definition of a limit. His verbiage is not particularly different from other aids to helping understand the definition, but simply saying "so what/all this is 'really' saying", does not help grasp the wording of the definition proper. [for the record, I didn't downvote the video. I'm not into such spiteful nonsense.] And when he expresses doubt concerning the claim that you really can't understand the definition until graduate studies, he is rubbing salt into the wounds of people who come through this video expecting to finally understand it. I'm not interested in his graph. I've seen those 'helpful' demonstrations before. I _do_ know intuitively at this point "what the definition is trying to say". What is lacking in people is the ability to parse the language of mathematics in real time, and I'm afraid that skill is akin to sight-reading a new concerto at the piano; and at the highest levels, read the score in an armchair and _hear_ the violins, horns, woodwinds in your mind.

[@Trynnagetmydegree__]

i agree and I wish I accepted my acceptance letter to UCSD :(

[@adude4524]

@@-danR can you use the limit of a function to find where i asked?

[@paolorodriguez2640]

He's right it's not that hard, it's just you thinking it is hard, a litle advice: if you're studying mathematics you really need to focus on it, remember that the brain cannot focus on two or more things at a time, so say you're studying a concept while thinking it is hard at the same time, you won't get any progress my friend, just focus on the concept nothing more. This is from my own experience :)

[@thabolikotsi5765]

Thanks I'm currently doing that with Real Analysis is my biggest challenge yet

[@lolopcallulu3082]

Yes! Fair point

[@Goose____]

who thought KZbin comments can have gold?

[@abizek4905]

💯

[@chideraugbonta4021]

💯 ❤

[@amanimotloung796]

You’re honestly the best. I wish I could take all my school fees and just give it to you because you make me understand much more in a video than my teacher can in a week

[@conflicted0076]

I have a calculus exam tomorrow, i may fail. But finally being able to understand this gave me some comfort. Pray for me y'all!

[@thebestking4615]

Hey, one month late but hope you did well

[@mattkelley9110]

How was it?

[@animalworld3759]

A year after im in the same situation now guys, i have it in a couple of hours, pray for me ❤

[@prathameshjoshi2539]

patrickJMT is love, patrickJMT is life

[@ashleynelson5855]

::) u hpjh buttock CAN

[@thebatoul8831]

Accurate

[@cataclysmicbane9068]

When I graduate and start my career I'm going straight to patreon and giving you the biggest donation ever!

[@christianleyva3166]

how did it go, did you graduate?

[@cataclysmicbane9068]

@@christianleyva3166 believe it or not I graduate on May 20th! I’m finishing up my final semester right now. Thanks for keeping me accountable for something I said so long ago. I will follow through!

[@cataclysmicbane9068]

@@christianleyva3166 I will be graduating this May actually! Almost there. And I will fulfill my promise.

[@CarlosSanchez-wn8gr]

Did you graduate ?

[@alergames147]

Did you graduate?

[@blessinggorengecho3973]

I no longer go for lectures. ever since i discovered the legend...patrickjmt!!

[@Jonathanjumps]

10/10. I read through my textbook, and all of the resources my instructor provided and got nothing but this really put it all together in words I could understand!

[@darbaram4303]

THANK YOU! idk why my professor started teaching the entire concept of limits by throwing the definition at me but you just saved me so many tears

[@sophita_]

Thanks for the video :) I didn't really understand the definition of a limit before, I just memorised it

[@patrickjmt]

+Sophie Grace you and me both! :)

[@-danR]

@@patrickjmt 0:46

[@metawhirl4609]

@@-danR I am studying with this book too. Same here bud

[@screamingisbeter]

Great explanation. I bought a supplemental calculus book which omitted this section because it's based on "high level mathematics." Think people underestimate our ability to learn sometimes. Will definitely be supporting your videos!

[@patrickjmt]

thanks! glad i could help!

[@projectjt3149]

Dude, don't even get me started with how most colleges omit the proof for Euler's identity

[@RozzanaRose]

This is a massive help! My professor is used to teaching grad level calculus, so he gets easily frustrated with us even though it's the entry class 😅

[@mariambobat]

Patrick. You are awesome. Understood this definition after a year. I wish you could make real analysis videos. Such explanations are very clear. Your teaching style is unmatched. Thank you!

[@vijayisbrown]

i wish you were my math professor.

[@didar-dissectingecon5976]

It’s by far the easiest explanation of this definition. Thankful to you!

[@lulabelr-s5697]

I watched this video to help with honors real analysis at Stanford University this is def the best video on this subject thank you so much you're amazing

[@ZuhaaFatima-gw7mj]

finally found a KZbinr who can teach calculus in simple words 🎉

[@alessandropietro3285]

After two days of trying different materials & feeling an idiot, you have finally let me understand this definition. You clarity is just impressive. A huge, huge thank you from sunny Italy!

[@patrickjmt]

thanks so much for the kind words! was able to visit italy once, briefly, 10 years ago. hope to make it back there one day. some of the best food i ever had was while there!

[@MANOinTECHNICOLOUR]

I've been watching your videos for a few years now. I would not have passed any of my classes without you. You're the best teacher I have ever had. Thank you so much Patrick.

[@catherineferris4379]

LOVE LOVE LOVE your videos!!! I am a math tutor myself so I felt discouraged when I did not understand this topic, but you made it sound so much easier!!!! THANK YOU PATRICKJMT!!

[@saulcoria8679]

This actually really helped me! Thank you so much! I tried to learn from watching Sal from Khan University but it just wouldnt click. You are a much better teacher, thanks again! :)

[@patrickjmt]

thanks! glad i could help you out!

[@gretawilliams8799]

Saul Coria That guy is a QUACK

[@basicnpcc]

Thanks mate! This made perfect sense. Props for teaching it in such a way that you encapsulated the definition into pieces that actually make sense to the average person.

[@FellaSack]

You're actually amazing, I can't understand what the hell my calculus professor is talking about for 2 weeks, and I come here, watch this video twice, and understand just fine, THANK YOU!

[@patrickjmt]

happy that i could help you :)

[@ChefFarisMom3]

You made the whole concept clear to me ... My teacher should learn from you 👍👍👍

[@LGND-ry6dk]

6 years later and you’re still helping poor confused college students. thank you for your service brother

[@avatarthelaststeambender8565]

Thank you for explaining the variables epsilon and delta in simple way. Now I know that epsilon correlates to the limit (L) on the y-axis and delta correlates to the x value it is approaching (c) on the x-axis! I hope you have a nice day!

[@xrees]

My man... you have a way with words... best video ever. Thank u

[@MetalAsBalls]

You make magic out of red and black sharpies on white paper! Your lectures become so simple and intriguing!

[@ryankbr]

Brilliant video! This helped demystify epsilon delta proofs so much for me!

[@bbtishia1]

Thank you so much for the explanation!! I was reading it in the book and had no idea what it was talking about! Thanks to your video, I understand it better!!

[@kaleabdereje-m4y]

haven't seen anyone on this platform that teaches as good as you

[@patrickjmt]

thanks so much :)

[@lumiere4460]

*Mind Blown Gif* This video really just blew the lid off the case for me. Things are so clear now.

[@Sen-hr8qv]

Oh my god. This makes so much more sense now! I was so confused with that intimidating definition but you broke it down to its core and really cleared things up for me! Thank you!

[@BB-yg4fp]

Getting ready for a grad program where I need Calc I as a pre-req, never took calculus before so I'm using Udemy to bridge the gap, and you just saved me after being baffled by a couple components. Thank you!

[@hayden6700]

Never seen this concept explained so well, thank you

[@derekmcanally11]

For my Calculus kids watching this: a is the same thing as c.

[@bobbysteakhouse7022]

Thanks Mr. McAnally!

[@caninci7379]

derek gibe de pussi b0ss

[@TacoSt8]

thanks very much Mr anally

[@mryup6100]

@@rubico1894 you uncultured swine

[@hunterpruett5455]

Thanks Mr. McAnally

[@Tony-nl6pf]

Thank you. I'm taking calculus online and you helped a lot.

[@ajanjua9924]

Man i didnt understand this since last 2 weeks.This video helped me alot understanding ....thanks👌

[@Htwolg02]

Thank you for the video! This is the section we are working on in Calc 1 and you cleared it up so well. Keep doing these!

[@patrickjmt]

Perfect, glad it helped. It is a confusing topic when you first see it so I was not sure if the video would clear anything up or not!

[@UAa320]

+patrickJMT thanks Patrick your videos have always helped me, especially now that I am taking calc 1 this definition of a limit concept had me confused. But with your video it makes sense now.

[@eyoeldiress7852]

this video literally saved my life.keep doing your thing; i really like your videos.

[@josonkimmargarethp.5651]

U LITERALLY JUST SAVED ME FROM BREAKING DOWN. GOD BLESS

[@aguirretrinidadenrique1372]

You're amazing! Thanks bro! I don't understand the Spanish videos and I found one of your videos and they're really good! You were my last opportunity

[@ysz7423]

Covered 2 of my math class, combined is 100 minutes and made perfect sense, which for some reason my math teacher just can not get this thing straight. Thank you

[@erikeriksen1617]

At 8:15 really helpful to me, and therefore maybe to you, around the time where he starts the sentence with: "and thats the whole point....."

[@lungilesithole6143]

You're amazing @patrickJMT . You're help is a major contribution to my studies and for that I thank you. Keep it up

[@azyle2104]

Got it in the first watch , you're brilliant .

[@TheEmilysvergara]

YOU MAKES THIS SO EASY FOR ME TO UNDERSTAND THANK YOU!!❤

[@denisholi2705]

Awesome man. I also was stuck on that. And when I see your explanation it got all clear..

[@rendi1555]

Thank you, I've realized what limit is mean only watching your videos . Thank you again for your usefull explanations

[@姜芃越]

It's intuitive while still maintaining the rigor, thank you!

[@mittens3claire]

THANKYOU SO MUCH!!! just saved me on my calc test tomorrow!!

[@PaingPaing-li5cj]

I know that this video was posted 8 years ago, but I want to say thank you for this video helps me a lot.

[@patrickjmt]

Glad it helped!

[@roopaalmeida7958]

I appreciate your heart to teach it in a simple way

[@jzmina]

I watched your video after trying Khan academy. Yours honestly helped me out way more. Definitely using your videos in Calculus next semester. Thanks! ^-^

[@mmgm868]

Thanks a thousand times I was struggling on this topic. Thanks once again

[@rimuru-kun_x_ciel-chan]

God tier explaination, I had a general idea it was meant to be like this but it solidified my understanding that it si supposed to be like this but I need to next see examples to fully cement the ideas

[@patrickjmt]

well all need examples! glad it helped

[@rimuru-kun_x_ciel-chan]

@@patrickjmt yes, it explained what I sort of intuitively knew but didn't understood in a way that I can explain it in words

[@daniellejdevlin8882]

This video REALLY helped me! Thanks so much for posting this.

[@msfreya777]

You are an amazing teacher, I got the intuitive idea.

[@patrickjmt]

Wonderful!

[@ecemteknik3750]

thank you so much!!!! i was really confused after my first calculus 1 class then i found that video. NOW I UNDERSTAND IT!

[@patrickjmt]

Glad it helped!

[@smergle11]

Thank You!!! This is definitely the best video explaining this concept

[@amy_muk]

Thank you for this! So relieved to finally be understanding this after about 6 weeks!

[@wongamzamo8232]

Man you're a legend , thanks for simplicity!

[@patrickjmt]

my pleasure :)

[@silversharky3258]

Dude u r a lifesaver....hats off... would really appreciate if you could do a series on Real Analysis 😊😊

[@1829Emily]

Thank you for this video! it made the concept so much clearer. all those symbols make it look harder than it is

[@patrickjmt]

it is a bit confusing for most everyone when they first encounter it. it definitely is not mechanical and takes some 'thinking about' to understand.

[@andrewkina9611]

You are awesome parrickJMT!!! Got a lot of help from your videos!

[@ThaoNguyen-yb6xq]

Yes you should be impressed with your self. Thank you for this!

[@Soccerforlife_10]

Great job. I got it. Very well explained! Be proud of yourself. Gonna send you 3 cents a day!

[@scummybabyelephant6094]

This is explained SO well like OMG !!!! Thanks you soooo much❤️❤️❤️❤️ I hope your quarantine is going well

[@patrickjmt]

glad you like it! quarantine is a bit boring but not so bad overall :)

[@marinafileva8953]

So great at explaining, wish you were my professor!

[@loquatrose2010]

You are a legend! Thank you for making these videos.

[@yeboahphilip8114]

best tutor ever..well done sir

[@tumak1]

Excellent presentation! Kudos to you. Cheers

[@maribelruiz9683]

MADE PERFECT SENSE! thank you thank you thank you Patrick

[@phantom_drone]

I am starting to understand this. Thank you!!!!

[@ramachandraraonanduri4043]

I really love the way he explains it

[@devarapallivamsi2981]

thank you sir...!!m i was really searching for this.. for a long time..!!!!!!!!!!!!!

[@shahadalenezi2548]

Thank you thank you thank you ❤️ watching you from Kuwait 🙏🏻

[@m__a_]

My professor explained that in class, and I was like "I have no idea what that definition is trying to say" then I watched this, and now I'm good hahaha... Thank you!

[@fati4274]

Mayerley sameeee

[@sajidsheikh9984]

Really same case is here with me 😋😋😋😂

[@绯橘衣-s8g]

Thanks for the video :) it really helps me to understand what im learning currently.

[@patrickjmt]

glad it helped!

[@绯橘衣-s8g]

i have some difficulty of some questions but i dont know which video of yours i should watch to solve the question... could u tell me how to message

[@vaibhavbhandari8661]

an actual legend amongst us

[@osamamansoor927]

Understood this on first watch, you're amazing. ;-;

[@zulfazlihamjah8897]

wow your explanation really make sense😊

[@gauranshbaveja335]

Thanks man. This is so well-explained!!!

[@lucasargandona4658]

3:20 that inhale was very deep xD. You are the G.O.A.T btw

[@markkaradimos9482]

Thanks! I'll check out your videos on how to use this definition to determine limits of various functions.

[@jeromeambaliza8133]

Thank you for this very helpful tutorial.

[@tarekzaki1]

PatrickJMT you are awesome, please keep going

[@sophiazhang7556]

U r such an amazing math teacher!

[@tharindugamage3467]

This is so helpfull. Thank you so much to Distribute your knoledge to us😀😀

[@stormyork8178]

Thank you for this video! I am currently taking calc 1 over the summer and we just started doing limits. I come across multiple problems like this in the book and they didn't make any sense to me. Although I'm still not certain on how to do these problems, your explanation made it more clear! I was also wondering if there is anyway that you could upload your notes/demonstrations onto a pdf for students to download and use for help?

[@mjallan123]

Yes! Please make a lot more videos like this. Also things like continuity, differentiability, etc..

[@Myrslokstok]

Yes please, agree!

[@patrickjmt]

+Bad MF i already have those topics. a ton of them

[@mjallan123]

Really? Like the definition of continuity/differentiability/integrability etc Rolle's theorem? MVT?

[@patrickjmt]

yes, i do. just search

[@mjallan123]

Excellent, I will :)

[@ritikchail7330]

Very well explained with the use of graphs

[@mostexpensiveeverything3866]

Thanks a lot buddy ...this video cleared everything...keep up with the good job.

[@sheruloves9190]

U explained it so differently, gr8. Thank you

[@marypreethi5272]

At last I understood the definition😁. thank u sir😊

[@TheEsteemedSirScrub]

Wow! Fantastic explanation! I totally got it!

[@mukarit_code]

Awesome and useful video. Thanks so much.

[@Alexis.j3nni]

Thank youuu you’re the besttt