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What exactly is e? Exploring e in 5 Levels of Complexity 

Dr Sean
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To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/DrSean . You’ll also get 20% off an annual premium subscription.
What is e? Let's explore the number e in 5 levels of complexity, ranging from compound interest, to representing e in calculus, to simulating e with probability.
This video was sponsored by Brilliant.
00:00 Introduction
00:12 Level 1: Compound Interest
02:30 Level 2: Probability
03:38 Level 3: Calculus
05:43 Sponsor Message
07:00 Level 4: Pascal's Triangle
09:17 Level 5: Simulating e

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5 июл 2024

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Комментарии : 91   
@DrSeanGroathouse
@DrSeanGroathouse 12 дней назад
To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/DrSean . You’ll also get 20% off an annual premium subscription.
@mohammadmorshed4684
@mohammadmorshed4684 11 дней назад
This man explains math in such an intuitive way and his videos are rlly high quality, but he only has 15k subs. Actually underrated fr
@ExtraTrstl
@ExtraTrstl 11 дней назад
For real. This is some of the most accessible and coherent explanations. Dude is one of the best teachers I’ve ever had.
@2kchallengewith4video
@2kchallengewith4video 11 дней назад
A very underrated math channel for sure
@Tristanlj-555
@Tristanlj-555 11 дней назад
One of the rare times “underrated” is used correctly:)
@westongunningham7151
@westongunningham7151 10 дней назад
I'd just like to say I followed him before 5k
@AdityaPutatunda
@AdityaPutatunda 10 дней назад
Agreed! The same way your comment needs some vowels
@AntoNqnt
@AntoNqnt 9 дней назад
I have a presentation for an important exam in literally 2 days that is exactly about the number e, as well as the exponential function; and a video such as this one truly is appreciated edit : i went crazy with it tysm
@user-jm9tf3uw1p
@user-jm9tf3uw1p 9 дней назад
e is the most insane number I have ever seen. I started learning it yesterday and I was shocked when I realized how versatile e is. For example the derivative of e^x is e^x and e^((x^h-1)/h)=x as h approaches zero
@Simpson17866
@Simpson17866 7 дней назад
You can approximate e to 18 trillion trillion decimal places using the digits 1-9 once each :D (1 + 9 ^ (-4^ (7*6)) ) ^ (3^2^85)
@linuxp00
@linuxp00 7 дней назад
My favorite representation is the Taylor's Series, because it relates e with sine, cosine, i, pi, sinh, cosh and hyperreal calculus. Also, as an infinite series you're mind blown when you see that it's derivative is really itself!
@kavehtehrani
@kavehtehrani 11 дней назад
I'm a math graduate and I find your videos to be educational even to me! Keep up the good work the quality is top notch my friend!
@DrSeanGroathouse
@DrSeanGroathouse 6 дней назад
Thanks so much, I'm glad to hear that!
@SeanRaleigh
@SeanRaleigh 11 дней назад
Both levels 4 and 5 are mind-blowing. Well done!
@bemusedindian8571
@bemusedindian8571 8 дней назад
Level 5 was mind blowing. Never heard this before.
@DrSeanGroathouse
@DrSeanGroathouse 6 дней назад
I'm glad you liked it! It's probably my favorite
@DanielC618
@DanielC618 11 дней назад
Great job! By far the best explanation I found 👏👏👏let's get that RU-vid algorithm going, this channel needs way more exposure!
@Fire_Axus
@Fire_Axus 10 дней назад
no
@hamedajab2483
@hamedajab2483 11 дней назад
Quality is absolutely crazy
@NicholasAngelidis1
@NicholasAngelidis1 11 дней назад
another great video!
@randyzeitman1354
@randyzeitman1354 9 дней назад
Superb. Far away, the best explanation of e.
@randyzeitman1354
@randyzeitman1354 4 дня назад
e is far more important than pi. Pi explains how many straight segments make up a circle. e explains how those circles integrate into reality itself.
@S-payanage
@S-payanage 11 дней назад
A letter duh
@nahuelsotomayor32
@nahuelsotomayor32 20 часов назад
Literally just e, why make it harder
@moonwatcher2001
@moonwatcher2001 4 дня назад
Excellent, interesting and amene!!!
@eliteteamkiller319
@eliteteamkiller319 8 дней назад
I love this channel so much.
@DrSeanGroathouse
@DrSeanGroathouse 6 дней назад
Thanks so much! I'm glad you like it
@guglielmotranchina249
@guglielmotranchina249 5 дней назад
McLovin's smart doppelganger
@SobTim-eu3xu
@SobTim-eu3xu 11 дней назад
Great video, I love it❤
@geraltofrivia9424
@geraltofrivia9424 2 дня назад
Great content
@jaymethodus3421
@jaymethodus3421 9 дней назад
E as I use it: Exact; Equivalent; Expression (energy), e^i for 'computational cost' but the most [E]vil way I use it, as to denote exponential constant values, for scaling of base 3/4 calculation expressions into self-similar real-number ratios of irrational "digits" being operated on logarithmically.
@AndrewDangerously
@AndrewDangerously 9 дней назад
Can you explain this at level 1 and 2?
@jaymethodus3421
@jaymethodus3421 8 дней назад
@@AndrewDangerously It would require an exponential amount of text. Do you describe that 'amount' of that text using units derived from paragraphs? from words? from characters? From sentences? Pixel on/ off rate? The various electrical circuitry quantitues, taking their own exponential functions into account of this unknown value exponent? See, 0,1, and 2, are not real. 3 is where the real value baseline begins, as far as the instructional code for reality. 012 is a *continuum constant* that acts as a function instructing relative operational order of value exchange between real quantities. Dimensions aren't real. Yet trigonometry is extremely correlative to the deep-scaling of that very concept. Idk what to call my theory yet, but seems to be very well supported by every stone I turn over in my expansive search.
@jaymethodus3421
@jaymethodus3421 8 дней назад
@@AndrewDangerously Uhh. I tried... So 1^2 is 1. Terrence Howard really screwed me on this shit ngl lol.... but he's crazy. And I'm both/neither. He is onto something deeply irreducible about the discrepencies of '1', '0', and 2; to the exponent of the discrepancies from using -=X/ as our 4 highest order "math operations". 1 is actually an irreducible scale unit that represents an infinitely irreducible and unique value composed of higher and lower order integral values as they are ALL, mutually calculated. In %base10linear: 1=sqrt(-2)
@jaymethodus3421
@jaymethodus3421 8 дней назад
@@AndrewDangerously How's that for level 1 and 2? Pun intended lol
@jaymethodus3421
@jaymethodus3421 8 дней назад
Terrence has glimpses and he's high EQ, he knows what he saw, and he just runs with it. But he has no idea wtf he's talking about it what it actually means, or when and where to actually appy it without sounding like a snake oil salesman.
@andrealves6545
@andrealves6545 11 дней назад
The last one took me by surprise ahah
@DingleTwit
@DingleTwit 11 дней назад
The derivative part of level 3 made me literally put down my book and go “whoa” when I read it. That’s the version that finally made e click for me.
@Fractured_Scholar
@Fractured_Scholar 5 дней назад
Care to do a Level 6 for Rotors?
@Neodynium.the_permanent_magnet
@Neodynium.the_permanent_magnet 11 дней назад
Yeah, baby, yeah!
@jeremyi4693
@jeremyi4693 11 дней назад
In high school calculus, our teacher taught us a mnemonic device for the approximate value of e. Think of a picture of Andrew Jackson in a square frame with a diagonal line from one corner to the other corner. Andrew Jackson served 2 terms, he was the 7th president, he was first elected in 1828, because he had 2 terms, we use 1828 twice. And the angles in the frame are 45-90-45. So, 2.718281828459045
@bsbrawl1653
@bsbrawl1653 11 дней назад
😮 cool
@ianbennett2443
@ianbennett2443 11 дней назад
unfortunately, i know more about integrals than i do us history
@andyghkfilm2287
@andyghkfilm2287 9 дней назад
Agh but what if I don’t know what Andrew Jackson looks like??
@jeremyi4693
@jeremyi4693 8 дней назад
​@andyghkfilm2287 think of a square with the name Andrew Jackson written in it.
@carultch
@carultch 5 дней назад
@@andyghkfilm2287 He's on the most common printed bank note of US currency. He's Mr $20 Bill.
@infinityleleveling
@infinityleleveling 9 дней назад
There are more ways to intuitively think about e. My favorite is the “e is the image of 1 by the exponential function” approach. But for that to really make sense, you would have to really understand what we mean by the exponential function and its many definitions. The exponential function can be defined as the inverse of the natural logarithm, but I find this definition to be superior: the only function whose derivative is equal to itself and is 1 at 0.
@Skellborn
@Skellborn 11 дней назад
I'm sorry, i dont get the Limit at 5:30: e^x lim((e^h-e^0)/h) is 0/0 for h-> 0. Meaning you have to do l'hospital. But dir this you have to differentiate e^x and you start all over again. How do you know it's 1? By stating it 1min earlier?
@joelganesh8920
@joelganesh8920 11 дней назад
As stated in the video, the limit is the definition of the derivative of e^x at x=0, which was already assumed to be 1.
@sachavalette1437
@sachavalette1437 5 дней назад
exp is the reciprocal function of ln so its derivative is 1/f’(f^-1(x)) = 1/(1/exp(x)) = exp(x). This is how to prove it.
@yawninglion
@yawninglion 8 дней назад
I was expecting the final level to be some circles in the complex plane.
@orologioimpazzito
@orologioimpazzito 11 дней назад
Why you look like Sheldon´s brother 😀
@carultch
@carultch 5 дней назад
He doesn't look anything like Georgie.
@orologioimpazzito
@orologioimpazzito 5 дней назад
@@carultch 😪
@fractodacto
@fractodacto 11 дней назад
cool
@RobertoCarlos-tn1iq
@RobertoCarlos-tn1iq 8 дней назад
a medical doctor and a mathematician! congrats!
@ElGnomistico
@ElGnomistico 6 дней назад
*E*
@rikisanity6045
@rikisanity6045 11 дней назад
Engineers: e=pi=3
@assassinraider442
@assassinraider442 11 дней назад
e
@carultch
@carultch 5 дней назад
Integral z^2 dz From 1 to the cube root of 3 Times the cosine Of 3 pi over 9 Is the log of the cube root of e
@willie333b
@willie333b 10 дней назад
👀
@gaigor
@gaigor 10 дней назад
@delta9990
@delta9990 11 дней назад
e > π calculus > geometry i will die on this hill
@sebas31415
@sebas31415 11 дней назад
What about Calc 3 and 4 which touches on geometry (as in proof of area, surface area, and volume formulae)
@danmiltenberger5616
@danmiltenberger5616 11 дней назад
2.718 is not > than 3.14.........
@unicorn3232
@unicorn3232 11 дней назад
@@sebas31415 that is barely geometry tbh, and that's actually fun
@Cow.cool.
@Cow.cool. 11 дней назад
Abstract linear algebra > calculus any day
@hydropage2855
@hydropage2855 11 дней назад
@@sebas31415I’ve definitely seen you before somewhere else. Another gd player
@Fire_Axus
@Fire_Axus 10 дней назад
why sponsor this video?
@JJW410
@JJW410 9 дней назад
So he can earn money?
@Lolwutdesu9000
@Lolwutdesu9000 11 дней назад
Nice video but at 5:40 you skipped why the limit simply equals 1. You can't just wave your hands and make it so as the limit tends to 0/0.
@joelganesh8920
@joelganesh8920 11 дней назад
As stated in the video, the limit is the definition of the derivative of e^x at x=0, which was already assumed to be 1.
@S-payanage
@S-payanage 11 дней назад
Otters 🦦
@CallOfCutie69
@CallOfCutie69 День назад
e
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