e - Euler's Number (MIT Lecture Video)

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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.

dktchr

e = n^n / (n-1)^n for n --> infinity

jarekk.

What percentage of modern society understands this level of intelligence ?

batmansboyfriend

interesting but you have to know the trick about logarithm and limits, also its hard to grasp because its purely algebraic allthough very beautiful though twist towards the end. much more easy would be the graphical way (draw a simple exponential function and work your way from up there)...

mathemitnullplan

I have very serious reservations about the use of the word “infinity”.
Infinity doesnt close the loop.
For practical applications….. ok maybe, but in reality the “closed loop” seems more like a plugged gap that doesnt describe the intersection correctly.
I have no clue about math though so what the hell do I know. 😅

stephenstuart

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

jethrobo

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.

thelastviking

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

putinscat

Why didn't he use binomial expansion

svs

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

nodirbek

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

grad

Did he just derived e with it already present there?

diabolicnephilim

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.

sproutssupport

e - Euler's Number (MIT Lecture Video)

e - Euler's Number (MIT Lecture Video)

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