Hi, Kalid
I am from China, and I found your amazing article through a translated version. I was confused on e for a long long time until spending 2 hours on this page, thank you very much!
I have a further question, maybe you answered before, that is “What is the essence of the a in a^x?” When a=e, you explained here, but what if a=2, a=10?
Is there some intuitive explanation?
I will keep reading your other articles:)
Best Regards!
Dewei
@Sonali: You’re welcome – I’m really happy to hear about the enthusiasm! A lot of the time we think “I’m not good at math” but it’s really just the way the material was presented.
Its a nice explanation and helps me to understand what is e
Thanks very much for writing this page. It really helped me a lot. I’ve been looking everywhere for a definition of e which I could understand and I’ve finally found it here. Your explanation was the best.
Could you please make this point clear to me?: I have read in Weakipedia that the importance of e is due to the fact that the exponential function e^x is equal its derivative. Besides, “e is the unique real number such that the value of the derivative (slope of the tangent line) of the function f(x) = ex at the point x = 0 is equal to 1.” as written there.
Could you explain in simple words this concept? What does for a function mean to have the same derivative as its original function? why is it important?
Someone (Anonymous, Nov 22) have first post here "e is the unity of diferentiation/integration. What is the concept?
My language is not English, so I am not sure to make me understand.
Thanks a lot!!
Thanks Khalid. I am reading all your articles and planning to buy a book on kindle as well. Your articles have made me interested in maths. Otherwise I have always thought that I don’t like maths and am poor in maths!
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Hey Kalid,
You should have one of those icons for sharing your articles on facebook. I think every math student in the world should see these.
Great work!
[…] 昨天我读到一篇好文章，它把这个问题解释得非常清楚，而且一看就懂。 […]
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Thanks for the video. I’ve never really understood e but now it makes more sense
@desiree: Thanks so much for the note! Making explanations “humane”, as you said well, is something I really hope to achieve . I appreciate it!
AMAZING! Forget textbooks and wiki, this is my new favourite go to website! Incredible!
thamk you for your intuitive explanation kalid
it helped a lot
Fantastic article that I am very happy I stumbled on. Very, very well done. I took calculus in college and still didn’t have any idea what e represented until today. Thanks!
Hi Kalid,
Thanks for such a clear intuition. Before I understood e only from analytical point of view. e was just an magical irrational number such that exponential function (a^x) with base e would have tangent line with a slope equal to 1, hence these nice properties and ubiquitous usage.
I wonder if there any intuition on “opposite” sequence that leads to e:
(1+x)^(1/x), x->0 ?
Thanks,
Nazar
I would like to ramp up the article production / teaching this year.