Precise Definition of a Limit - Understanding the Definition

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Precise Definition of a Limit - Understanding the Definition.
In this video I try to give an intuitive understanding of the definition of a limit. Be patient, this is often a tricky topic so I try to explain more instead of less!

[@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]

💯 ❤

[@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.”

[@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?

[@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?

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patrickJMT is love, patrickJMT is life

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::) u hpjh buttock CAN

[@thebatoul8831]

Accurate

[@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

[@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!

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[@CarlosSanchez-wn8gr]

Did you graduate ?

[@jonathanleverenz6838]

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!

[@vijayisbrown]

i wish you were my math professor.

[@blessinggorengecho3973]

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

[@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.

[@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.

[@mariambobat3227]

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!

[@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 😅

[@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!!

[@ZuhaaFatima-gw7mj]

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

[@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

[@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

[@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

[@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!!

[@lungilesithole6143]

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

[@didar-dissectingecon5976]

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

[@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!

[@ryankbr]

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

[@lumiere4460]

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

[@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

[@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!

[@xrees]

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

[@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! ^-^

[@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!

[@amy_muk]

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

[@MetalAsBalls]

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

[@Tony-nl6pf]

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

[@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

[@eyoeldiress7852]

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

[@aguirretrinidadenrique1372]

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[@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!

[@ajanjua9924]

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

[@andrewkina9611]

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

[@rendi1555]

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

[@user-gy7su8ti9e]

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

[@ChefFarisMom3]

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

[@daniellejdevlin8882]

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

[@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?

[@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

[@tumak1]

Excellent presentation! Kudos to you. Cheers

[@denisholi2705]

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

[@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

[@ThaoNguyen-yb6xq]

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

[@TheEmilysvergara]

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

[@mattm4162]

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 :)

[@mostexpensiveeverything3866]

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

[@josonkimmargarethp.5651]

U LITERALLY JUST SAVED ME FROM BREAKING DOWN. GOD BLESS

[@loquatrose2010]

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

[@silversharky3258]

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

[@yagnapatel3912]

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

[@evanflynn9956]

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

[@mlamuliphungula8827]

Great video! Now I understand haha, thanks! Your videos have been really helpful.

[@mmgm868]

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

[@mittens3claire]

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

[@roopaalmeida7958]

I appreciate your heart to teach it in a simple way

[@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.

[@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....."

[@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!

[@maribelruiz9683]

MADE PERFECT SENSE! thank you thank you thank you Patrick

[@tharindugamage3467]

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

[@wechiri1998]

thank you sir! needed this for my logic and reasoning class!!

[@devarapallivamsi2981]

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

[@markkaradimos9482]

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

[@marinafileva8953]

So great at explaining, wish you were my professor!

[@ryanguenther708]

Such a great video, thanks for the awesome explanation!

[@jeromeambaliza8133]

Thank you for this very helpful tutorial.

[@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 :)

[@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!

[@msfreya777]

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

[@patrickjmt]

Wonderful!

[@azyle2104]

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

[@charlespribyl7075]

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

[@TheRamzi39]

Thank you for this video your explanation is amazing very informative.

[@gauranshbaveja335]

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

[@wongamzamo8232]

Man you're a legend , thanks for simplicity!

[@patrickjmt]

my pleasure :)

[@TheEsteemedSirScrub]

Wow! Fantastic explanation! I totally got it!

[@sheruloves9190]

U explained it so differently, gr8. Thank you

[@tumusiimebrian3745]

Thank you so much Patrick

[@ritikchail7330]

Very well explained with the use of graphs

[@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.

[@ziggy8757]

perfect explanation.. got it instantly

[@JimmyEatsAbyss]

Awesome Video! Really intuitive

[@davidb4509]

Thanks for this video. This is still fuzzy, but I’m getting there. Thanks for the help. :)

[@williamsheppard6361]

bro. this was so helpful. thank you man

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Thank you sir!!Your videos are too good😊

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

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I really love the way he explains it

[@yeboahphilip8114]

best tutor ever..well done sir

[@yenbinh2239]

May i ask why we have to use open interval and can we use closed interval ?

[@user-lz4tm3nv5i]

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

[@patrickjmt]

glad it helped!

[@user-lz4tm3nv5i]

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

[@marypreethi5272]

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

[@rye_on_toast]

Your videos are so helpful!