e - Euler's Number (MIT Lecture Video)

Credits to Professor David Jerison (math.mit.edu/d...)

[@dktchr3332]

It turns out one needs to watch the whole video to understand where e comes from. He actually starts out constructing how one obtains the derivative of any exponential expression and "discovers" e in the process, i.e he "backs into" what e is by determining its existence, although its exact value is not known, and can't be because its irrational. He then uses e because of its mathematical properties, not its numerical value. In the end he demonstrates a mathematical way to approximate e's numerical value derived from its previously noted properties. A very elegant lecture and worth watching in its entirety.

[@nikimilky]

Yea when i learned about e we started with proving the existence of e then went the way up to derivetives. Does anyone have a link to the full lecture? Would like to see where it comes from

[@mohamedbenkhalifa1299]

I would love to watch the full lecture too

[@jethrobo3581]

For the absolute best explanation - watch the video of Eddie Woo when he defines e (Euler's Number).

[@svs4305]

Why didn't he use binomial expansion

[@nodirbek3272]

OMG. Concept of lnx built on number e. But he calculated number e using lnx. What the f. is he doing here?

[@putinscat1208]

Yeah! That makes no sense to me. Using Taylor series with x=1 ends at e, I believe. Euler may have stumbled on this another way when looking at compound interest. 1+1/1!+1/2!+1/3!+1/4!+1/5!... If I was gonna calculate e by hand, I would do this.. If we use calculus to discover relations that we need for calculus, it's cheating.

[@putinscat1208]

How can we discover e, by taking ln of anything?

[@thelastviking2039]

Yeah this is like precalc trying to explain what a binomial distribution is by saying “just plug it into your calculator”. There are way more and better ways to explain this.

[@jattysankar8151]

Excellent teaching

[@XCHtopia]

Full video kzbin.info/www/bejne/b6eVZpqdZ9Z9j6csi=aaDd8MFJm_Bk8HsC

[@fuluching]

ok, this is epic

[@divyamanify]

Excellent!!!

[@diabolicnephilim2659]

Did he just derived e with it already present there?

[@nickr7437]

That's what I said when I saw this. Maybe I'm missing the point, but I'm not sure what this proved.

[@camarques]

No, by definition the derivative function is df/dx = 1/(deltax) *(f(x+deltax) - f(x)) . So when he subtracts 0 (ln1) he can replace all that by the derived of lnx with 1 as the base point, and turns out all that is 1.

[@jacobstrength3945]

In a sense, yes! The natural log and logarithm properties were discovered and defined before e. All of these properties were provably true, and they knew e was some constant that had its famous properties, they just didn’t know what that constant was equal to. This video is in deriving how to calculate that constant.

[@RoyChadwick51]

What percentage of modern society understands this level of intelligence ?

[@grad8990]

I have a question. How did he go from the [1 + 1/n] to ln[1 + 1/n]?

[@hadial-mokdad5322]

He did not go from that to that he solved the latter seperately and then simply raised e to the ln of the limit which is equal to the limit (e^ln(lim)=lim)

[@thakurv1]

He’s asking why

[@putinscat1208]

And how can we use ln to discover e??

[@grad8990]

@@putinscat1208 This is right. I don't see any interest in this proof.

[@DemetrioAlbidrez]

When is Break time ?? 😂😂

[@sproutssupport7789]

Ouh god,what he calling that formula.That what he doing is correct.But his explain of"e" isn't correct.And that formula is called Indenitty.Because he using E,the name of phonex and his started Name .And He what doing,it was for his added negative number"1" but how he get 0.That isn't correct and E we got for fuse(cosX)+i(sinx) and we got E.But how we can fuse cosX and sin X.so we have the function of fuse positive and Negative numbers.Positive number is 2,5,8,11... And negative 3,4,6,7,9,11... And we got e(i,π) but we got 3 so we need to over his Formula for negative 1 to be equal zero.And you over his indenitty.

[@putinscat1208]

Euler calculated e using something like Taylor series with x = 1. As for sin, cos, you need to take the Taylor series approximations for them and relate to Taylor series for e^(ix). I used KZbin to see this in action. It would almost be nice if math teaches went thru the history of these things.

[@snakehawk8164]

Killamajaro = e

[@rudrakshdua5730]

Nice video sir