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In this video, we explain where Euler’s number e = 2.71828… comes from. We start by studying the example of compound interest, and use it to generalize e to being a constant that describes continuous self-referential (exponential) growth.
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E is a constant like the speed of light.
This video is about 22 minutes and 17 seconds too long😄 e just represents a continuous change that is 100% proportional to its current size. It's really that simple. In nature you'll never witness perfect 1-1 (100%) continuous compounding growth just like you'll never get a real circle that is exactly equivalent to pi. Things in our sundry world are just shadows of the Forms!
For newcomers, you can start watching at 16:45, which is when he begins to talk about e specifically. Before that he's essentially just calculating at a rate that is not 100%.
One more thing, the use of self-referential in this video isn't actually better than exponential. 2x is also self-referential. When it doubles to 4 (current size), the next iteration becomes 8. e is only different because it doesn't grow twice itself in discrete steps. It grows twice itself constantly!
e is the unique scaling constant set as base that makes the derivative of an exponential function equal to the function itself.
Not a very good explanation of how e is derived. Too much excess junk.
he used logs in an explaination for e thats not allowed
Many thanks for explanation, helped understand.
"e^1" when valued (2.718) is the LINEAR annual growth of an entity P at 100 % interest. added linearly to P
*e^j1" when 1(cosine (1) + jsin (1) ) is the CIRCULAR annual growth of an entity P when 100 % interest is added in QUADRATURE with the entity.P
Do not go home until you finish. Reading the value of E
I feel like this explanation is a bit incomplete because it doesn't address the meaning of e raised to complex or imaginary numbers.
Which doesn't fit neatly into self referential growth or decay intuition.
The reason we chose 100% was because if it was 50% or 25%. The derivative of e^x would've been 0.5e^x or 0.25e^x. That would've made finding the derivative for ln(x) or a^x harder. Especially the Taylor series for them.
Wow. I've been looking for an explanation of e like this for years. Thanks to this video, I finally understand what e really is fundamentally. Excellent video! Subscribed.
e is just when u multiply a infinitesimally small number larger than 1(1.00 00….1)an infinite number of times
Can you elaborate on the log base e of ln part? That part ocnfuses me
Thanks.🙏
This may actually be one of the best explanations of E.
He makes the statement that others can not describe Eulers in a sentence…then he tries to describe it for 23 minutes without actually making any reference to it.
Euler's number is the base needed for an exponential function to always equal its own derivative. In other words, e is the base needed for an exponential function so that the rate of change of the function value for any given "x" is equal to the function value itself.
Thanks! At last I've understood it! (e^x = lim(n->inf)(1 + x/n)^n)
This video is good for intuition, but you didn't prove that the sequence converges. All you did was show it's growth slows down past a certain point, which, I suppose, you couod argue deomonstrates a finding of a delta for which there always exists an epsilon which delta minus d is less than — for any possible x, because you just add on smaller and smaller decimals to the prexisting decimal, thus, I guess, proving, by epislon-delta definition, that the infinite limit of the sequence (1+1/n)^n is in fact 2.718… = e.
Bernoulli discovered it, not Euler
Excellent explanation. Very intuitive
Over complicated.
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Machine learning
Don't explain sthg you don't know you are an embarassment
I enjoyed your explanation of a very important number "e". I like the Multiplicative Factor equation of (1 + 1/n)^n to arrive at Euler's number ✏ … It can be a little confusing to understand the "natural log" relationship to Euler's number.
I guessed it right near the beginning. It must a sign the lesson was good.
E is that quantity whose derivative is itself.
brilliant video. I would just add "… growth at the natural maximum rate of the 100%" at the ending of your definition.
That was a super-intuitive perspective on e. Next, how did e^ix come to represent points on a unit circle?
That is the wildest pen grip I've ever seen
2.718
I’m sorry, but I’ve taught this for almost 15 years, and even I didn’t have a clue what was going on or where we were going.