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
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
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.
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?
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!!
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 :)
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.
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
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)
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?
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.
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 UA-camrs.
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.
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🎉🎉🎉
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.
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.
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.
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?
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
Getting rid of the limit near 5:51 with that justification isn't actually rigorous. The way you perform the substitution here isn't strictly valid, since you would have to introduce the limit for e with a different limit variable. So you'd have an h1 and an h2. You can swap around some of the limits using continuity arguments. But in order to perform the combination of the two h's into a single limit variable you have to demonstrate uniform convergence to the limit first. I realize that an epsilon delta proof (to show uniform convergence) might be a little out of place for this audience, but I am sure there are other ways to show what you were trying to demonstrate that aren't so hand-wavy.
2:52 Actually, e is called Euler's number. Euler's constant refers to a different number that is approximately 0.577... (denoted by a lowercase gamma, γ).
Spent hours trying to understand what is eulers constant and got it straightaway by looking at this. Thanks a lot.
Good
That’s great but in terms of its properties I’d go much further
@@vortex6132any good videos?
I rly understood every
thing in this vid but the factorisation of p
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
The explanation feels like getting an eureka moment every 5 seconds or so. Realizing all the connection you've learned in math
Fr!
@@manavgupta2059what does the F =? What about r? What they equal?
@@THE_HONOURED_ONE_LOL shut up
I WAS VERY HELPLESS ON UA-cam TO FIND OUT A RIGHT VIDEO TO LEARN THESE LESSONS. THEN THIS ONE CAME. THANKS A LOT. LOVE FROM INDIA
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
and it is a part of the connection inbetween the Harmonic numbers and Factorials, so that's neat.
Euler number, Napier constant is e. Oily-Macroni constant is gamma.
@@69erthx1138oily macaroni
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.
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?
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
@@dipteshrai5979 Profound! So it seems there's nothing fundamental beyond the number 0 and 1. Does this imply the binary representation?
@@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.
@@dipteshrai5979 Yes, your idea is very impressive! I agree with you.
Wow! You virtually connected various aspects of mathematics in a very interesting way! Thank you!
Doesn’t get better than this when it comes to explanation. Thanks!
I wish I had UA-cam when I was in college. I graduated with a BS Aeronautical Engineering in 1986.
This video is incredible. It is well explained and clear. Never seen so much professionalism and precision in a video like this. Thank you!! 🎉
Finally a clean video Thanks!
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!!
anyone still confused here?
Yeah me😅
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 :)
@@manavgupta2059 no need now! I have understood it well
Me too
Always!
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
Yes, most students never know where does this stuff comes from, as " but that way they can't see the beauty in it.
This is great. I never understood where the decay function y=e^-×ln (2) actually came from! Fantastic thanks.
Amazing video, you managed to perfectly explain e and ln in 12 minutes.
I’ve had problem with this concept.But after watching this, all my doubts are cleared now. Thanks a ton.
I'am a senior in high school and this helped me so much when working with these functions in math and physics
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.
It is not the best in any way lol
3blue1brown is best
Now what are u giving me because u lost the bet?😊
The best explanation for 'e' I've seen. Superb Work 😊
Brilliant explanation! Thank you. It clicked when you said that we want 1 as a constant.
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
So much potential in this channel as the way he teaches
Writing a test in a week about this topic, very nicely summarized
I am approaching an e^exponential headache, but it’s very interesting, thanks!
Brilliant video, cleared all my doubts 👍
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
wow.. very well- constructed video.. I like it when people start explaining from origins.. Thank you
heavily underated channel
this was so insightful, love all the connections you made, really helped me put it all together.
Mathacy, thank you so much. I ve been diggin from explanation to explanation without getting it.
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)
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?
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.
This channel deserves subs at the rate of e^x!!
What a easy explanation 👍
I love your videos! Excellent explanations - they never made this clear in school! Thank you so much!
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 UA-camrs.
Thank you Mathacy !!
You explained this really well 👍🏼
A fantastic explantion of the relationships.
From France, that was verry interesting, nice job !!
mind blowing mathematics
I am from India i want to say that your video based on interesting facts
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
Also the proof of the derivative of ln(x) is incredible
Please start making more like this
U thought us calculus in the simplest way possible than any schools or coaching institutes did.
this video is very useful, very very good, I hope it gains more recognitions
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.
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🎉🎉🎉
simply a wonderful explanation got it first time
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.
Another Masterclass as always! Thank You!
It could have been explained little slowly so that audience gets time to understand and catch up
Skill issue ngl
Great video ! Learnt a lot and beautifully explained !
Great work, things unravel like magic, amazing and precise. Thanks again. Differentiation of e^x, lnx, a^x . Nice and smooth
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.
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.
Hey, you are great teacher, dude. Thanks a ton.
Really well explained I enjoyed this video
🤓
5:44 that was cool i've never seen that derivation before
This video was great! Very informative!
Amazing video, it helped me so much!
What software do you use to make the animations? Or, do you code it all? Btw, great job.
This is beautiful
I will worship the exponential function right now, holy shift.
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.
Wooow mindblowing😍😍
OH MY GOD, this at the beginning of the video is what I was trying to understand. I'm shocked
Thanks for all your expressions
Thank you very much you're very skilled
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.
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
@@davidlixenberg5999bro really signed off a youtube comment with his name
@@SpaceWoodsIt's an ai
Excellent explanations. Thank you very much.
Really good video 👍
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?
It's just 2 ways of saying it
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
Thanks for the explanation, Squidward!
We never taughtt the derivatiion of thiis value.
Thanks.
This has the same feeling as discovering lost lore that's filled with plot twists
what a great channel!
I finally found the answer , i finally knew where logarthims come from
a log is an index
Very nice sir
Wow, just wow. Its beautiful.
My god what an excellent video!!
Very well done
great video - thank you
Really nice video. Thanks for your explanations.
Getting rid of the limit near 5:51 with that justification isn't actually rigorous. The way you perform the substitution here isn't strictly valid, since you would have to introduce the limit for e with a different limit variable. So you'd have an h1 and an h2. You can swap around some of the limits using continuity arguments. But in order to perform the combination of the two h's into a single limit variable you have to demonstrate uniform convergence to the limit first.
I realize that an epsilon delta proof (to show uniform convergence) might be a little out of place for this audience, but I am sure there are other ways to show what you were trying to demonstrate that aren't so hand-wavy.
Nice one, great job!
Amazing video
this is so amazing. thanks a lot
Excellent video... Could you please give me any hint of how I create animations with LaTeX formulas like you do?
Nice Vid
2:52 Actually, e is called Euler's number. Euler's constant refers to a different number that is approximately 0.577... (denoted by a lowercase gamma, γ).
I use to call It the Euler- Mascheroni Constant the last one
@@plaierdifortnaiti9955 The Euler-Mascheroni constant is another name for it. You can call it either name.
@@SsvbxxYT of course
Really👌🏻 clever 👏🏻👏🏻
Thank you for the useful content 🙏
Very good video
Subscribed!
I just don't get how you can conclude at 10:28 the derivative of a^x
Nice Video!
This was a great video thank you so much! :D
great video man!
what an amazing video