What is e and ln(x)? (Euler's Number and The Natural Logarithm)

[@angrwl]

Spent hours trying to understand what is eulers constant and got it straightaway by looking at this. Thanks a lot.

[@samueljehanno]

Good

[@vortex6132]

That’s great but in terms of its properties I’d go much further

[@Premium55]

​@@vortex6132any good videos?

[@abbasfadhil1715]

I rly understood every thing in this vid but the factorisation of p

[@nimo517]

I’m looking for one of those in regard to quantum theory and the applications in real world. I understand so far _it’s used on a micro scale when viewing the world, and small objects like atoms, and how the fundamental laws in nature do not apply any longer at the quantum level._ and I understand that concept, but that’s where I’m left in terms of my true understanding and faith in quantum theory. After describing the basic desires and principles of the study, I don’t really understand how the study is supposed to translate to real life. Then the thought experiments like the *cat in a box*? I sometimes think it’s just mental master***tion and all hypothetical talk. Sure I believe it’s provable on paper but to me I’m sooo close to getting it, but until then it’s like being a kid trying to pray and not knowing what to do

[@sw-reload9232]

The explanation feels like getting an eureka moment every 5 seconds or so. Realizing all the connection you've learned in math

[@manavgupta2059]

Fr!

[@THE_HONOURED_ONE_LOL]

@@manavgupta2059what does the F =? What about r? What they equal?

[@loanthebank9820]

​@@THE_HONOURED_ONE_LOL shut up

[@girlvermin]

@@THE_HONOURED_ONE_LOL for real

[@AimerBoy-t2z]

I WAS VERY HELPLESS ON KZbin TO FIND OUT A RIGHT VIDEO TO LEARN THESE LESSONS. THEN THIS ONE CAME. THANKS A LOT. LOVE FROM INDIA

[@finleycooper8844]

Just a heads up 'e' is Euler's number. Euler's Constant is a different constant (Also called the Euler-Mascheroni constant sometimes) and is denoted by a lowercase gamma

[@JunioSonicT.Hedgehog]

and it is a part of the connection inbetween the Harmonic numbers and Factorials, so that's neat.

[@69erthx1138]

Euler number, Napier constant is e. Oily-Macroni constant is gamma.

[@LukieReal]

@@69erthx1138oily macaroni

[@newsgo1876]

It is worth emphasizing that "e" is a number defined through the limit operation. And it happens to show an unique property in another limit operation, i.e. the derivative, that e^x has itself as its derivative. This is one of the wonders associated with the limit operation and the infinity process. Essentially, a number is just a symbolic name for a bunch of operations, except the symbols for the natural number 0~9.

[@leslyvalerianavarroberrone9323]

But what does it mean its derivative it's the same as the original function? As I knows, the derivative shows the growth rhythm for that function. Does it mean that the growth of f(x)=e^x is constant?

[@dipteshrai5979]

But 2 is an operation of 1+1 and 0 is 1-1. Is it not? And 1/ 2 is 1 divided by 1 + 1

[@newsgo1876]

​@@dipteshrai5979 Profound! So it seems there's nothing fundamental beyond the number 0 and 1. Does this imply the binary representation?

[@dipteshrai5979]

@@newsgo1876 well, I said that 0 is 1-1. So I’m saying, only 1 exists. Unless u want to think of 0 as an absence of 1, or an absence of anything.

[@newsgo1876]

@@dipteshrai5979 Yes, your idea is very impressive! I agree with you.

[@karimjanmohamed3835]

Doesn’t get better than this when it comes to explanation. Thanks!

[@emmanuelonah4596]

Wow! You virtually connected various aspects of mathematics in a very interesting way! Thank you!

[@sathyanarayananviswanathan3770]

I bet this is the best video about mathematics on youtube. I didnt even skip a single second, I enjoyed it entirely.... You just earned a new subscriber.

[@manavgupta2059]

It is not the best in any way lol 3blue1brown is best Now what are u giving me because u lost the bet?😊

[@nagarjun385]

Damn!!! These many years as a STEM Student, I've never ever got the finest and the most intuitive explaination of Euler's Number. Great video Mathacy. Good Luck!!

[@rickintexas1584]

I wish I had KZbin when I was in college. I graduated with a BS Aeronautical Engineering in 1986.

[@nacerwork]

Finally a clean video Thanks!

[@shyyongc.9477]

Very well explained video! Made the "e" great again, and really this should be taught in colleges/unis to get students understand the intuition behind

[@leslyvalerianavarroberrone9323]

Yes, most students never know where does this stuff comes from, as " but that way they can't see the beauty in it.

[@joelwyatt9949]

Amazing video, you managed to perfectly explain e and ln in 12 minutes.

[@Lordversus44]

This video is incredible. It is well explained and clear. Never seen so much professionalism and precision in a video like this. Thank you!! 🎉

[@jamesbentonticer4706]

This is great. I never understood where the decay function y=e^-×ln (2) actually came from! Fantastic thanks.

[@Jee2024IIT]

So much potential in this channel as the way he teaches

[@jesca4855]

this was so insightful, love all the connections you made, really helped me put it all together.

[@henrynwosu6277]

Omo. I hope I get to meet this man someday and thank him personally. Because you're out there giving meaning to my engineering degree and helping me see these things intuitively. Allowing me to chase my passion for Mathematics. Thank you isn't enough. Hopefully I can do something for you too. Thanks @Mathacy

[@elhatimimohammad6944]

I'am a senior in high school and this helped me so much when working with these functions in math and physics

[@mihisarakaveesha8954]

The best explanation for 'e' I've seen. Superb Work 😊

[@nithinsikinam]

heavily underated channel

[@aaronnanoo1887]

Brilliant video, cleared all my doubts 👍

[@frosted8229]

I’ve been searching for so long for a how e actually works this video explained it the best easily

[@0x90meansnop8]

Mathacy, thank you so much. I ve been diggin from explanation to explanation without getting it.

[@kennethchao1290]

anyone still confused here?

[@Aakash-e1x4t]

Yeah me😅

[@manavgupta2059]

Where did u got confused? I legit took 3 hours understanding this whole concept from this video and ran into lot of misconceptions So, I recommend u the following before watching the video: 1) Be expert with all logarithmic properties. (Solve 10 questions of each to master them) 2) Be expert with all exponential properties 3) Most importantly, learn differentiation first Then u will get second half of the video It is very complicated but once u understand it, it becomes very very simple :)

[@Aakash-e1x4t]

@@manavgupta2059 no need now! I have understood it well

[@saravananrajendran9813]

Me too

[@notreallydavid]

Always!

[@JASPREETKAUR-eo9oe]

I’ve had problem with this concept.But after watching this, all my doubts are cleared now. Thanks a ton.

[@aleenavirdee5656]

I love your videos! Excellent explanations - they never made this clear in school! Thank you so much!

[@block7059]

Writing a test in a week about this topic, very nicely summarized

[@RM-yv7zv]

I Just want you Let you know That I studied this for years back in high school and this is the first video made me understand what it means

[@boshraal-sheghri7821]

wow.. very well- constructed video.. I like it when people start explaining from origins.. Thank you

[@amrishravidas9258]

This video was super informative and it goes along great with 3Blue1Brown's video on Euler number. Also, at 6:26 the graph for x^100 looks a little off, isn't it supposed to be much steeper?

[@Mathacy]

Thank you for the kind words Amrish. As to the graph of x^100 and e^x, if x>648 then e^x > x^100. The main point of of that part is to show how dominant exponential functions are, so you can think of the x-axis scale as being very large.

[@Av-fn5wx]

This channel deserves subs at the rate of e^x!!

[@forpublicstuff728]

Brilliant explanation! Thank you. It clicked when you said that we want 1 as a constant.

[@morgangrenoilleau7430]

From France, that was verry interesting, nice job !!

[@indisingh2990]

Thank you Mathacy !! You explained this really well 👍🏼

[@mangeshjirapure9154]

What a easy explanation 👍

[@krishshah2209]

Another Masterclass as always! Thank You!

[@carlo70no]

I am approaching an e^exponential headache, but it’s very interesting, thanks!

[@josephhuelbig]

Energy can equate to Mass dissolving multipled by constant multipled by imagery vapor symbol representation squared E≠imc (-)E=(imc)² E≠(imc)² (-)E=imc² E≠imc² (-)E=((i)(mc))² E≠((i)(mc))² (-)E=mic² E≠mic² E=(mc/2πr)² E≠(imc/2πr)² E=mc² E=i In mathematics and physics, the symbol "c" can represent various concepts and constants, including: 1. Speed of light: In physics, "c" typically represents the speed of light in vacuum, approximately \(3 \times 10^8\) meters per second. 2. Constant: "c" can also represent any constant value used in equations, formulas, or expressions. 3. Circumference: In geometry, "c" often represents the circumference of a circle, given by \(2\pi r\) where \(r\) is the radius. 4. Center: In geometry or coordinate systems, "c" can denote the center point of a circle or other geometric figure. 5. Complex number: In complex analysis, "c" is sometimes used as a constant in complex numbers, such as in expressions like \(z = a + bi\), where \(c\) represents the real part of a complex number. These are some of the common uses of the symbol "c" in mathematics and physics, though its specific meaning can vary depending on the context.

[@exoticcoder5365]

this video is very useful, very very good, I hope it gains more recognitions

[@nassimzouaoui469]

mind blowing mathematics

[@amirjutt0]

Boy you make incredibly awesome videos😻 Awsome explanation.I suggest you to be active on this channel and gradually you'll be listed in top class KZbinrs.

[@kay_792]

It might be 12 minutes but its a valuable explanation of exponentials

[@sharibkausar-n8t]

I am from India i want to say that your video based on interesting facts

[@keftam]

A fantastic explantion of the relationships.

[@jimsvideos7201]

In the case of radioactive decay the mass isn't lost so dramatically, what changes according to that function is the concentration of that particular radioisotope. They all end up as Pb, some just take more steps to get there.

[@DiLLZGFX]

Great video ! Learnt a lot and beautifully explained !

[@iamtrevor1551]

Please start making more like this

[@dilipranade]

simply a wonderful explanation got it first time

[@Dinesh123lol]

Amazing video, it helped me so much!

[@User-54321n]

Hey, you are great teacher, dude. Thanks a ton.

[@ranjithamarakoon8842]

Excellent explanations. Thank you very much.

[@jayan99]

Great work, things unravel like magic, amazing and precise. Thanks again. Differentiation of e^x, lnx, a^x . Nice and smooth

[@davindersehmi33]

This video was great! Very informative!

[@nandakumarcheiro]

The graph of y=x swings between exponential power of e upto x and by inversion becomes a logarithm of x.By Lambert function this becomes a complex number w multiplied by e to the power w.This means a complex may swing between an exponential by the power w as well may become an inverse function as logarithm of a complex number.

[@ayokaniolubanjo344]

this was very very helpful was a bit too fast though as i had to keep processing so many things just said while listening to what is being said after it really rests on your previous understanding (strong understanding) of previous topics)

[@mathcrux407]

Hi. Your teaching method is very creative and smarter i want to learn from you. So please guide me how can i learn your methodology which software/applications you use to make that awesome videos

[@arjun_12]

U thought us calculus in the simplest way possible than any schools or coaching institutes did.

[@Mikerdlt]

Thank you a lot i have been watching lot of videos trying to understand better what is e and with your your explanation i got it in no time although im not a native english speaker🎉🎉🎉

[@er-s428]

This was a great video thank you so much! :D

[@nikkibhamra7536]

Really well explained I enjoyed this video

[@msag68]

🤓

[@ThreeDogKnightAZ]

Thanks for the explanation, Squidward!

[@aspektn.5066]

This is gold. Wish I had time some day to use pencil and paper and write as I watch.

[@jayking2011]

In 8:56 you can't cancel out something unless if its using multiplication. That is using addition so you can;t cancel it out.

[@CATel_]

We can write (x+h)/x as (x/x)+(h/x) and there, x/x canels out to 1. So therefore, we get (x+h)/x = 1+(h/x) Hope my explanation makes sense!

[@tommypaul501]

It could have been explained little slowly so that audience gets time to understand and catch up

[@gamingdude7959]

Skill issue ngl

[@YorangeJuice]

5:44 that was cool i've never seen that derivation before

[@liaoweien]

this is so amazing. thanks a lot

[@enzoys]

I just don't get how you can conclude at 10:28 the derivative of a^x

[@octs609]

at 8:57 (x+h/X) why would x cancel? it is because the ln of x+h is the same thing x times H and therefore all over x would mean x cancels and thus it becomes 1+h? I am confused someone let me know.

[@CATel_]

We can write (x+h)/x as (x/x)+(h/x) and there, x/x canels out to 1. Therefore, we get (x+h)/x = 1+(h/x) Hope my explanation makes sense!

[@kayihanthescientist6881]

Really nice video. Thanks for your explanations.

[@saltstillwaters7506]

Thank you very much you're very skilled

[@gulnaroguz2510]

Worthy brain burned video! 🔥 thanks a lot!

[@fetch7312]

proving the limit as n approaches infinity of (1+1/n)^n is such a fun excersize tbh, recommend it to anyone who wishes to try it

[@fetch7312]

Also the proof of the derivative of ln(x) is incredible

[@Zackarius]

I will worship the exponential function right now, holy shift.

[@lemonmorning4204]

Wow, just wow. Its beautiful.

[@Humbertofxl]

My god what an excellent video!!

[@comcilliak]

great video, thank you. Coming from numberphiles video of e however, i am a little confused - wouldnt it be eulers number and not eulers constant? Which is supposed to be something slightly different?

[@Mg_887]

It's just 2 ways of saying it

[@ARS-fi5dp]

Thank you for the useful content 🙏

[@yassinenajar4369]

This has the same feeling as discovering lost lore that's filled with plot twists

[@mosab643]

What software do you use to make the animations? Or, do you code it all? Btw, great job.

[@vytg706]

what a great channel!

[@rektspresso7288]

OH MY GOD, this at the beginning of the video is what I was trying to understand. I'm shocked

[@chackken]

Nice one, great job!

[@Jadem4]

Nice Video!

[@jsingh6931]

Really good video 👍

[@ShaunakDesaiPiano]

5:47 what is the justification for using the same letter in the e limit? Shouldn’t we use a different letter?

[@mugincoffe]

It is the same letter, because it is delta X

[@jononeill5684]

great video - thank you

[@genesis553]

Wooow mindblowing😍😍

[@matematicacommarcospaulo]

Excellent video... Could you please give me any hint of how I create animations with LaTeX formulas like you do?

[@Oscar-vd4cv]

Seems like he uses logarithms to define logarithms. I'm sure this video could be useful, but I'd have to watch it over and over and slow the speed.

[@davidlixenberg5999]

I found the video much too fast and when all the different k's were exchanged for different values along the grraph of e questionable. David Lixenberg

[@SpaceWoods]

@@davidlixenberg5999bro really signed off a youtube comment with his name

[@Sammysapphira]

​@@SpaceWoodsIt's an ai

[@joerob5917]

This is beautiful

[@algorithminc.8850]

Fun channel. Thanks. Subscribed. Cheers

[@LepusCompositions]

amazing video!

[@AstroKnowledge114]

Subscribed!

[@eclipsehorizon7655]

I finally found the answer , i finally knew where logarthims come from

[@mensamoo]

a log is an index

[@Eds0n2021Gamer]

great video man!

[@0Christ1]

Thanks for all your expressions

[@sukhibhamra5750]

Really👌🏻 clever 👏🏻👏🏻

[@dylanalexander5163]

what an amazing video

[@vidyadharkottisa8367]

Too good. Excellent. Thanks