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Near the end of the lesson, one of my students asks a question about why the values start turning around 0.4 - I made a couple of videos that explain this phenomenon: www.youtube.com/watch?v=cDbnP... (Part 1) and www.youtube.com/watch?v=a0ePX... (Part 2)

Main site: www.misterwootube.com

Second channel (for teachers): trshow.info

Connect with me on Twitter ( misterwootube ) or Facebook ( misterwootube )

Maybe they do realise it lmao. Good teacher.

100%

Had a teacher like him in highschool, he was amazing and really cared about us students and even related it to real life. Everyday looked forward to his class as it was very engaging.

@David Chang Oh ya that's why most of them got into teaching in the first place. Its the huge paycheck. That and the fact that the kids and their parents are always so reasonable and great to work with. The kids pretty much teach themselves.

How tf do you know whether or not they appreciate him? What did you expect them to stomp on their desk and shout, “O captain’ my captain!”?

Despite being a 3rd year maths undergrad and already knowing everything said in the video, I still watched the whole thing. This is a really fun way to introduce limits to the students. Maths is such a beautiful subject and I really think if more teachers were like you a greater proportion of students would take an interest in it. Hats off to you

It also gets very difficult and confusing very fast. The concepts, notations, long definitions, jargon- it is the exact reason you have to be VERY passionate about math to grasp all of it correctly. Many people simply dont have enough patience and foundation to understand it beyond school level.

F

@James Doll You should be receiving notifications when a user tags you. That’ll make it easier. ;)

@MouseMan Sorry it took so long! Only found out today that I could see all of my old TRshow comments, so been digging through and checking em out lol

@James Doll Thanks for responding!

I love how he literally stopped his whole class for the sake of the one kid who had stopped paying attention, and the kid who told him to get off his phone sounded legitimately angry. I feel like this guy has succeeded as a teacher because of the fact that he has his students so engaged and he cares enough about the individual to stop the class to allow them to regain their focus. These are the teachers we need more of. Its always refreshing to see a teacher who genuinely cares and also tries to make learning fun, while at the same time trying to make the content he gives to his students more easily understood. He simplifies things as much as possible in order to benefit everyone in his class, and I think that deserves tons of respect.

@Emenesu I get what you mean but I think it depends. Oftentimes the one kid who doesn't getting is just echoing the general sentiment in a more vocal way. I've seen corrections to wrong statements come through thanks to this.

Stopping a class for one kid is horrible. Been there, done that, and absolutely hate it. A perfect teacher has everyone focused, all the time, without trying, which is very close to what this guy does, except for that one occasion. Stopping the whole class makes everything awkward. Some of the best teachers I had in school just let the kids go without penalties, so instead of being bored out their mind, they could just leave. Turns out that's exactly how university works, and uni classes are by far the best and most relaxing out of all types of classes.

@Unixtreme Just as you could have proofread your comment, students are responsible for their education, too. Those most responsible are the parents though, and you get out what you put in. The fact that salaries are frozen at a flat rate, basing raises only on time employed, certainly prevents those wanting to teach, to teach. If they had the opportunity to excel and earn more, they’d look for employment there. That’s why private schools have great teachers. Simply put, just like anywhere else in the private sector, you do well at your job, you earn more. If a teacher knows this will not occur, the drive isn’t there without an inner passion, and the mediocre ones stay. There would be a desire for schools and teachers to excel if parents could choose where their kids attended school, as well. It would be difficult to recruit families to a low performing school… if choice was present, that would cause low performing schools to do better. The most important piece of all of this is though, we are responsible for our own education, how much we get out of it, and it certainly is not the government’s job how well we do.

@Dori Gunderson Bellan this is an incredibly ignorant take. Education isn't no reason, it literally the pillar of society. Why do you think education sucks so much in the US?? Because even by right wing meritocratic views those who could be good teachers would rather work on something else. I don't subscribe to this ridiculous believe but even by that logic it's obvious that not paying teachers well damages education. There's a very direct correlation between countries that pay teachers well and how well educated people are on average. And I'm not saying bad teachers shouldn't be fired, they should, but if you don't pay shit you won't get good teachers. Only for those who can pay for expensive private schools which again is not a good foundation for society and its why on average the US (and the UK really) has so many uneducated people.

“0 to the power of paying attention?!” -sun tzu the art of math

perfection cubed

Just the way he said that without missing a beat. That was brilliant.

Kid has been forever immortalized on YT for not paying attention

No mere words can describe how good of a teacher he is. I've always been avoiding maths, but he makes me feel that maths is actually interesting.

@Bảo dont worry. studying is a continuous process. it wont stop until your brain cells starts to decline in numbers (as you start losing memory, motor functions, cognition aka grow old) its only a matter of whether you wanna accept new information or not. you can say studying has an exponential growth so past a certain level of information you will start to see things a lot more clearly and you will pick up new informations more quickly and that often results in information overload which is why many geniuses out there have very peculiar traits or hobbies to distract them from information overload.

@List unfortunately, I realized this after graduating high school and my major has no relations with mathematics whatsoever , but I can still enjoy his videos so maybe, it's not so bad after all

Studying is interesting. The sooner you realise that, the better.

To say that maths are interesting is an understatement. I had to start studying math on my own to see that though.

i would just like to say i’ve met him and he’s the only teacher ever that made me excited for math

I'm too. He make the math's lession so interesting!

@T L b ib

yo we had a teacher during our pre university. he was very enthusiastic. well versed in mathematics and physics. graduated from the most prestigious college of my country and he could have joined an industry and been a great asset to it, which he kinda did. but then later, he resigned and decided to teach as that was his passion; to guide young minds towards science and engineering. and boy, he did. he inspired us, a few classes before and after us. he retired 4 years back. he was a legend and i am sure each and every student of his will remember him with a smile, cos he left a mark so strong. feel so proud that we had him and feel sad for those who didnt. eddie woo reminds me of him

0^0 is not = to anything also negative numbers are like -1^-1=1/-1

I had a math teacher at the university who was so passionate about his teachings. He always made time for his students. we could knock on his door and ask for help and he'd sit with you one on one for a while and really help you and explain things. Thanks to him I managed to go from a C in the first year to an A in the last year. We need more people like this :)

i love his energy in the class , he is an amazing teacher , I felt exactly like I was present in the class !

Small correction at 13:04, it should be lim as x→0⁺ (from the positive side) since the limit on the negative side doesn't exist with the definition of exponetiation used for real numbers.

@Hareecio Nelson Proof: x^(-n) = x^(n-2n) = x^(n) / x^(2n) = x^(n) / ( x^(n) * x^(n) ) = 1/x^(n) At least that's my solution to prove it. Feel free to point out mistakes

@Rex Schneider not at all. "Apart from open intervals, limits can be defined for functions on arbitrary subsets of R (Bartle & Sherbert 2000)" "The limit of f, as x approaches p from values in S, is L, if for every ε > 0, there exists a δ > 0 such that 0 < |x − p| < δ and x ∈ S implies that |f(x) − L| < ε." [Notice that we only care for x's in S, for which f is defined. For any other points, they don't matter.] "This generalization includes as special cases limits on an interval, as well as left-handed limits of real-valued functions. [...] It also extends the notion of one-sided limits to the included endpoints of (half-)closed intervals, so the square root function f(x)=√x can have limit 0 as x approaches 0 from above."

@Irrelevant Noob You claim: "Not true about the domain needing to include generic regions AROUND the point" That's simply wrong. Go find any formal definition of a limit and you'll see that it starts something like this: *Let f(x) be defined for all x≠a over an open interval containing a.* Limits are only meaningful to establish a value at x=a if the function is defined on an interval *containing* a. You can never use the sort of one-sided limit you're proposing to produce a value for the function at the limiting point.

@Rex Schneider wdym "no"? The fact that the OP said in the middle of the text something, DOESN'T mean that they didn't ALSO include what i quoted. (That part is true, agreed. Sure, your extrapolation is also true, but it's not available in the context i was highlighting.) Yes, you're correct about who i was replying to and what my correction was supposed to say. But not about the domain i was using. And it wasn't just me, as i already said Martin had also only been looking at that "restricted" domain. Also, restricting a domain to R+ and taking the limit at zero ISN'T nonsensical, the limit is supposed to look at (the parts of) neighborhoods WITHIN the domain. 2. Sure, but i was talking about disadvantages of expanding the domain in the general case for any function, not just in this specific case of a discontinuity. That would still be there in either domain, so it's neither a pro nor a con. Therefore it's a non-issue. And i'm not "relying" on graphs, i'm just pointing out that for C->C we can't really use graphs to quickly evaluate a function like we can for R->R functions. Not true about the domain needing to include generic regions AROUND the point. There's limits for endpoints of intervals, which work since they will only use the values of the function only for the parts of the region for which the function is defined. :-B 3. My problem is that you said "(-1/2)^(-1/2) = (-2)^(1/2) = i.√2" when it should've been ±i√2, etc. And you cherry-picked only those examples that use simple roots, when there are a LOT of worse-behaved values that wouldn't be as easy to dismiss (or select a representative value from the multitude of available powers).

@Irrelevant Noob 1. No, the OP of the thread merely claimed that the "the limit on the negative side doesn't exist with the definition of exponetiation used for real numbers". Which is true. But it's also true that the limit doesn't exist with the definition of exponentiation used for complex numbers either. You were replying to the poster who asserted "No one ever defined the process when exponent is negative anyway", which we all know is erroneous, but your "correction" was trying to claim that "no one ever defined the process when the exponent is a non-integer AND the base is negative". Right? I'm just telling you that the _process_ when the exponent is a non-integer AND the base is negative is well defined in C. So somebody was able to define it when the exponent is a non-integer AND the base is negative. So it seems you're the one who wants to impose R+ as the domain for a function when you're trying to take a limit at x=0, which is patently nonsensical. 2. Discontinuities are a real issue if you're attempting to find a limiting value for a function at x=a when the function is discontinuous at x=a. You're going to have to stop relying on graphs. A limit of f(x) is only defined at a value x=a when the domain _includes_ the region around x=a. So how are you going to find a limit at x=0 without a domain that includes the region around 0? 3. What's your problem with multi-valued functions? The function x^x has an infinite number of negative x values where it is multivalued, and they get denser as x→0-. That ought to be enough of a clue that the value at x=0 is indeterminate. I gave you examples of the function having real, imaginary and complex values. They are called examples, not cherries. If you find it puzzling, maybe you should try to come up with a few non-integer negative values of x where x^x isn't multi-valued? Please feel free to cherry pick and you should be able to convince yourself.

These guys have a very compassionate teacher and someone who is motivated to the students work and well-being making sure there having fun and learning at the same time, this is true learning!

13:56 For anyone wondering why this number starts increasing again specifically between .4 and .3, it's because the minimum value of x^x (x to the x) happens at x = 1/e, aka. the inverse of Euler's number, aka. ~.36788, which, as you would notice, is between .4 and .3. You're welcome.

@j gunther er no. It is one and explained fairly well in the review at the beginning of the video.

This made me anxkssious! So I had to know, and spreadsheet told me 0.3678795 is the exact turn (with 20 zeros after point) witch square is 0.69220062755535000000 (the zeros are raw results, I dont know if I would get it more precise with a spreadsheet that breaks the 20 digits after point). I must now test it this number has some aestethic relevance (beside gold proportion and 0,68...). Thanks!

@Kavi Ramyead Best answer

@hiidupiidu it's where the first derivative of x^x=0

One of the most useful comments here. Thank you! ❤️

I wish I had a teacher like this, I love how passionate he is and always teaches us with a smile. The students must be grateful

Eddie, I love your honesty about why where the turn around started at a particular place, " I don't have an answer for that". But you sure have made math fun. I have used math for all of my professional life, but you make it worth studying for leisure time as well.

You’re one of the best teachers I’ve ever heard teach, I already enjoy math but I’m sure if you were my teacher I’d like it even more.

Loved your videos, Mr. Eddie. Thanks for the effort and the amazing pedagogy. I immediately wondered, though: Lim (x->0-) x to the x is not defined, and hence you would agree the limit itself does not exist in the strictest sense.

If everybody had such great teachers the world would be different...

@ChäoS;PriSM i pity your math classes

This replies section is for smart people I am out.

@Fizzishin And like most higher-paid professions, it would also attract horrible teachers. It's not just as simple as throwing more money at the problem, but teachers probably do deserve more money for all that they put up with.

@Tawfiq Click hahahaha NO

This is the first time I've seen one of your videos. I have to say, you really know your stuff and are a great presenter. Bravo... great stuff, Eddie!

He shows them mathematically why 0 to the power of 0 can be defined as 1, which is cool, but I think its important to explain the significance behind it as well. We don't have real life situations that model an example of it, and in fact many mathematicians and textbooks will claim its undefined. However, calling it equal to 1 is very useful for not over complicating many other mathematical definitions that use series including a 0 term, and it helps solve the problem of discontinuity as well in such cases where we would otherwise have a hole. Its not the most perfectly accurate definition, but in STEM applications it is necessary to define it as such to avoid computer errors and to get the best answers.

This was a superb example of wonderful teaching. I'm a doctor so I quit maths ages ago and yet I watched this entire video with great interest and even understood it!! Really commendable

What a great teacher. I was absolutely blessed to have a phenomenal maths teacher for five years in high school, but then she went to teach kids in Singapore and my interest in maths died due to the piss-poor subsitutes that filled in. Teachers like this are a rare treasure

Teachers that love their jobs are so much better... This guy is awesome.

@Siddharth Raj yeah i highly doubt that

@Quader Nowaz no, you smell a person whose mind is stronger than you and you don't want to admit it and hence you're using a defence mechanism, ie. calling him nerd just to satisfy your feeble mind

@InsideOutside UpsideDown If my memory of school is correct, the school, my parents and the law were very insistent on me being there about 6-8 hours a day and I, still being underage back then, had very little say in the matter. Same applied to pretty much everyone else around me.

@Cameron no one put anyone in that room that didn’t want to be there

@InsideOutside UpsideDown Not someone that got left behind but if I put someone in a room that they didn't want to be in and demanded their undivided attention for an hour and a half while talking about something they aren't interested in (three to four times a day) I wouldn't expect them to still be listening a few weeks later.

This is emotional for me to watch. I asked my high school maths teachers why 0^0=1 and they said “it just does” or “don’t worry about it” or “you can find out if you do maths at university”. I did try to do maths at university but I didn’t get far as I was so far behind. I don’t blame the teachers, a lot of that was my fault for not working harder and also they were doing their best. But I wonder how I would have gone if I had had a teacher like Eddie. I guess it’s never too late!

@Water Bird You need to reread my response more carefully. Note that I said multiplying anything by zero must be zero, which contradicts how any base raised to zero must equal one. You are correct that x^0 is by definition 1, but the fact it is a definition does not preclude it from requiring consistency with other basic algebraic facts. It also does not mean it cannot be proven. The laws of exponentiation are what determine what x^0 means. Repeated factors doesn't make sense with x^0 but the division of powers law requires (a^n)/(a^m) = a^(n-m). If n=m then a^0 must equal 1. In order for exponents to be a well-defined operation we require x^0 to equal 1 via this law. It is also true that 0 raised to any power is equal to zero. Now x^0 and 0^x are both at odds with each other. One demands it has to equal zero while the other demands it has to equal one. So which rule wins when saying 0^0? Neither of them do. We say 0^0 = 1 by definition. Its OWN definition. Note that everything that has been stated here is DEFINED when the base is NOT zero. The laws of exponentiation, from which x^0 = 1 is true, requires x to NOT be zero per its definition. This means 0^0 requires its OWN definition however some mathematicians will combine these definitions to say they are true for ANY value of x, but strictly speaking it isn't the case via an argument of definitions. 0^0 is an argument of notation. You're making non-mathematical statements. For example "*" isn't a mathematical expression. * is something called a binary operator. It requires two operands. Simply saying "*" isn't a mathematical statement. Exponentiation is a fundamental component of algebra. The law of exponents isn't a "nice and useful pattern", it's a property inherent to our construction of exponents. Just like the distributive property isn't a "fun little pattern to memorize", it's inherent to our construction of the real number system. By the way, if x/x = 1 and x^0 = 1 then x^0 IS x/x. Also note that multiplicative inverses are also definitions.

@Michael Coulson I am talking about the literal definition of raising something to the power of zero not algebra or any paterns Anything to the power of zero is by definition the empty product since you are multipling no numbers which may sound weird but it's a thing that can be done x^0 is not x/x but nothing * nothing Or just * Algebraic patterns a nice and useful but they are not strict definitions

@Water Bird x^(-1) is defined as the multiplicative inverse of the number x. It means x*x^(-1) = 1. This would mean 0^(-1) is the multiplicative inverse of 0 such that 0*0^(-1) = 1. Any number multiplied by 0 will return 0 and yet the definition of multiplicative inverse requires a 1 to be returned, so how do you invert the operation? In this instance we arrive at 0 = 1 and thus we say the multiplicative inverse of 0 is undefined. In fact, this demonstrates why division isn't a true inverse operation of multiplication. One of the properties of exponents is such that (a^m)*(a^n) = a^(m+n). From this we could derive 0^0 = 0^(-1+1) = 0^(-1)*0^1. This is literally the multiplicative inverse of 0, again. Except now, instead of saying it's undefined, we say "actually that 1 sounds good after all, it obeys one of our rules of arithmetic" while conveniently ignoring the other rules it violates. All this achieves is to show that, algebraically, we cannot actually prove 0^0 = 1. In fact, it is *more accurate* to say that 0^0 is simply *defined* to be 1. That is to say it equals 1 "because I said so" or "because it just is" are both literally the truth. We can reveal our motivations for why we follow this *convention* and the conveniences it creates for our number system, but you cannot prove it like this video tried to claim or by appealing to some mathematical law that has to be obeyed.

most high scholl math teachers are not mathematicians - they are process followers - they can tell you what to do to get the answer but they have no real working idea why it works - hence “it just does”.

Truly an amazing teacher!!! What a treat to watch!!! 🔥🔥🔥🔥🔥

Very cool. Basically plotting a graph of the function: y = x^x It has a rather strange curve!

I LOVE this lesson. Thank you Eddie!

"0 to the power of are you paying attention?" mate that was brilliant

@Caged wrote “How do you not pay attention in this class?” Especially since 1) you’re paying for the class, and 2) no one is forcing you to attend. Oh, and 3) CHILDREN interrupt, grownups don’t.

@Zeesneakyninja The problem is that the little yawper was creating a distraction for those around them. I’ve been in classes with those kinds of annoyingly self-absorbed infants. It’s hard to pay attention when there are two people talking at once-especially when one of them isn’t saying anything worth listening to.

@Timothy McAlee, Sr. GeD I believe it’s still called the Reimann Hypothesis, not the Riemann THEOREM because it hasn’t been proven. But then, you do know the difference between a mathematical hypothesis.(i.e. a conjecture) and a mathematical theorem, right?

@Zeesneakyninja He is just trying to help them. By the time they realise that studying can be both interesting and useful, it will be far, far too late.

@Timothy McAlee, Sr. GeD Why haven't you claimed the massive prizes awaiting anybody who can prove the Riemann hypothesis ? Because you don't actually know, do you ? It is NOT proven to be true, but we have no no counter-examples. If you do not know the difference between these two things, you should not be teaching anybody anything.

When the teacher cares about the course their teaching, you get a way better educational experience and this guy demonstrates this perfectly

I'm so envious of those students... wish I could sit there in that class. I learnt all of these things said in this vid but never got to think that far or that specific way nor was I encouraged to do so... Mr. Woo is probably the best maths teacher I've ever seen

I never took calculus, but if I ever did you definitely seem like a good instructor to learn from. The only part of calculus I looked into was derivatives, because I was interesting in learning about artificial neural networks and you need to do back propagation when using assisted learning. Back propagation requires understanding derivatives to do.

14:22 I'd guess that the tipping point is 1/e, since the derivative of x^x is ((ln x)+1)*(x^x) and we need its derivative to be 0 for it to be the tipping point, which requires (ln x)+1 to be 0.

Thanks - this was great!

Hahahaha, that was entertaining...

If math is racist this dude is a math supremacist!

@Vector Can you smash Atoms ⚛️ of Sword of Wonder Woman .

Why aren't u making video nowadays

I watch you vedios

he seems like such a good teacher it makes me so angry to see students not paying attention to his classes at all

That was a fun video! My initial thought was that it would be undefined, which seems to also be one of the two possible answers. The reason for that is X^0=1 because any number divided by itself is 1. IE. X^2/X^2 = 1 is the same as X^(2-2) is the same as X^0 which therefore equals 1. But this causes an issue with 0 because 0^0 could also be written 0^2/0^2. For 0 to be divided by itself would be undefined. My calculator says this, "Undefined or 1".

Now that was a really good video. Thanks very much Eddie. The change in direction lies in the definition of the power expression - or its possible relation to say Log of ln ---- eg. m.Log(a) =Log(x), or x = 10^{m.Log(a)} ---- for the case m = a for very small m. As m becomes very small, x 'approaches' 10^0 ----- ie. 'approaches' 1. But ----- making 'a' become EXACTLY equal to zero is an issue, as it leads to an undefined condition or situation. Log(0) is a 'doesn't compute' situation. So it's possible that the function a^0 = 1 does not apply to 'a' being EXACTLY equal to zero. This means, the a^0 = 1 while not including a = 0. But for practical purposes, people could definitely say that a value of 'a' being ultra super close to exact zero could be considered as 'zero'. That's for practical purposes.

Since you are multiplying with variables, you should use the dot as the multiplication sign for no confusion. But also very nice 👌

I am 59 years old. I've had 100's of teachers in my life. This guy is about the best I've ever seen. Passionate, polite, patient & motivating! I hope his students in future classrooms appreciate, respect & award this guy! He deserves it!!!

Drop the "motivating". You're destroying your alliteration!

All for the cam

@The Koifish Coyote Yeah! That's the important one! 🤣

You missed one thing: funny

@Reena Oswal don’t be rude

You're an excellent teacher man. I wish I had a teacher like you for Calculus 2 before I gave up on math.

Eu fiquei maravilhado, esses alunos precisam saber o quão sortudos são por terem um professor como ele, eu nunca imaginei que alguém pudesse explicar de forma tão boa, eu tenho certeza de que nunca mais vou esquecer isso.

Wow. What outstanding teaching-drawing in the students (including me) by making something abstract into something more tangible and then including them collaboratively in the solution. And your passion for the subject is absolutely infectious. Thank you!

I don't know why YT recommended this vid to me today - but I really like how you included the class. As the lesson goes on - at least for my ears - you can hear the class (or a good chunk of it) getting more and more interested ^^ In the end I think the most important point is that this is a definition because of the limit we can observe. Coming along another path we could easily define the result in a different way. Because if we have 0^m / 0^m for m>1 this can be written as 0 / 0 (because 0^m for m> 0 is always 0) which is not defined (because multiplication is not bijective for something multiplied with 0 IIRC).

'I don't have an answer for that yet.' That is a sign of a good teacher. He's honest and even said he will have a look at it.

@Matisyahu Rua yes so tell my your doubts,let me clear it for you

The definition of a^x for any a=/=0 comes from the exponential functions and branch of logarithm (there are infinitely many different "logarithm" function that can be defined in the complex plane, because e^z, or exp(z), is a periodic function). Anyways, we define a^x for any a>0 as : a^x = exp(x * ln(a)) In the case a=2 and x=1, we have 2^1 = exp(1 * ln(2)) = exp(ln(2)) = 2.

@Roshab Shabor Well you're actually incorrect. As both are just opinions. You say potato I say potato.

@Richard Catterall Fair enough at least you can admit it's all subjective lol.

@lorrygoth I appreciate the charity you extended to me that's something rarely seen these days.

This actually made me very interested in learning about maths, why couldn’t I have a teacher like him?

I took all the advanced math I could in High school and my teacher was like this. She was in her mid 20's and had a very simular style. Everyone in that class took those classes because they wanted to be there as it wasn't required. We went to a small Alabama school way out in the country. I went to 3 Math Olympiads before I moved away my senior year, and everyone in that class who participated scored in the top 10% of the state for kids our grade. Thank you Ms Williams. These kids have a great teacher.

I was talking about this to my friends and explained it to them after watching this video. I think it’s mostly just unless we break the concept of infinity or something, or find a way around it, we’ll never know the answer. That’s really cool lol

For the question in the end, the derivative of x^x is (x^x)•(lnx+1). When x1/e, the derivative is positive and the function is growing, so when x=1/e, x^x reaches its minimum. Since 1/e ≈ 0.368, we see the function decreases when x0.4.

Great teacher, challenging students. Much respect.

@archimidis Well, I mean, that's literally what many other mathematicians agree with. So... I dunno m8, maybe you should complain to every mathematician who agrees with that and not only that guy that probably learnt it from someone else.

@John Doe Thank you

I am on my way to become a math-physics teacher like this guy

wow

Thomas Steele that’s it! I was trying to figure out th accent.

This video's so good at explaining the basic theory of limits that I keep coming back to it even though I'm almost done with my 2nd semester of Computer Science.

Very fun explanation. It can be proven with a series in calculus. We know that 1/(1-x) = Σ(x^n) from n=0 to infinity for all |x| < 1. If you set x=0, you're left with the equation Σ(0^n) = 1 for n=0 to infinity. That means that 0^0 + 0^1 + 0^2 + 0^3+...0^n = 1. Since 0^1, 0^2, etc... all evaluate to zero, it simplifies to 0^0=1.

So I am in college now - let me just say - this has to be one of if not the best high school math teachers out there. He is smart, confident, and knows how to give an engaging lecture. Wish I had a teacher like this in high school.

Interesting video. However, I guess I always regarded 0^0 as an indeterminate form because the left and right hand limits are not equal. Or, am I misremembering the rule about limits only being valid if the left and right limits were equal. Is the left-handed limit even defined since y=x^x is not continuous for values of x less than zero?

Omg, I would love to have you as a math teacher! You have so much enthusiasm and you actually get around to somewhat trivial questions like this.

El Psy Congroo

Bitch How every teacher is like this in highschool/College/University not primary school tho.

SoberBro i know right

noobenstein No, you’re the one who is wrong. Most of mathematics is not physical. Mathematics isn’t meant to make physical, and most of it doesn’t. π is very-well defined. We can approximate it only because it is well defined, since ill-defined or undefined objects can’t be approximated. The fact we can approximate PROVES it is well defined. It is not much simpler than this. I’m sorry you can’t understand such a basic an obvious principle of mathematics. It goes to show you’ll probably never be a mathematician anyway, which is fine. By the way, if your Mac computer yielded that (-0.001)^(-0.001) was approximately -1, then you either typed something wrong, or the program is glitched. Like I said, you can conclusively prove it goes to 1 from every direction.

noobenstein Also, infinite numbers are a thing. They comprise an entire field of mathematics and are very useful in set theory. Read on George Cantor

I remember way back in 69 when I was in high school, our math teacher told us that anything to the power of 0 was 1. Being sceptical brats at the time, we asked him to prove it. This he did on the blackboard with an eager flair and proved to us with math that anything to the power of 0 is indeed 1. Best math teacher I ever had!

Hey Sir :) I was wondering if the reason why the limit (im not so sure) doesn't go below 0.693 which is it's minimum point is because according to the law of the limit it will always equal 1 and anything below 5 cannot be rounded of to 1. Please do correct if I misunderstood :)

This video has me listening and finished it. Wow. Amazing. I wished I had a lecturer like you. Awesome~!

After rewatching this after a few years, I just now realized the missing piece on the left side, where a =/= 0 should have been a condition. At least for the a^m ÷ a^n => a^0 if m=n (coz you can't divide by zero). Without the restriction, it breaks down. Hence the limit definition makes more sense.

He could have just said: "it's 1 remember it, it'll be on the exam" , and continued, but he's done more: he gave them meaning, passion, curiosity, knowledge. The fact people hate Maths, or anything for that matter, it's because they learn it from the wrong people. It's because some doctors, or business men, could have been good teachers and they chose to be something else to make the money they think they deserve. I hope this teacher continues to be the same and contaminate his students with his passion.

Its good he did not say that because it would be wrong. 0^0 is not 1 since x^y with x,y -> 0 does not have one unique answer. If y = 0, then x^0 -> 1, but with x = 0, 0^y -> 0.

@Pratyush Well, tbf, it wasn't really explained in this video either. According to what I found, It has to do with the mathematical rules of 'power', though it doesn't really equal 1, it's considered an undefined number between 0 and 1. It's still a big debate why 0^0 should equal anything when there is no real mathematical evidence for it other than convenience in equations, which is what it's mostly used for. In general 0 is a poorly implemented and explained number, they always say stuff like n x 0 = 0 because "0 is always nothing", then change the rule when it suits them, the use and meaning of the number is quite inconsistent.

@Chetna Singh If a requirement for being a teacher was you needed to be omniscient, then there would be no teachers. Nobody has, or ever will have, all the answers. People can only teach you to the best of their limited ability and knowledge, how much you learn from them is up to you.

teaching is a difficult job (if done properly) that requires a lot of education and is paid an absurdly small amount. its understandable why people wouldnt want to do it. its very easy to burn out when you dont get the compensation you should, have to deal with kids all day and then the state decides to make your job even more difficult by giving you too few lessons or making the classes absurdly large.

He could've, but then he'd be lying. Its *not* 1, it's undefined

he's a great teacher! I've never been this interested in a math lesson in my life (or interested at all), he clearly loves his job and I wish he was my teacher

This is very interesting i've always found 0^0 undefined because 0^1/0^1 would be the same thing as 0/0 which equals undefined

I am in my seventies but my passion for maths remains. I have to admit this teacher is amazing. I was lucky to have such a passionate teacher.

This is one of very few teachers who get me to watch a math video in my free time. He makes it interesting and exciting

If only my secondary school maths teachers were as enthusiastic as Eddie. Great video.

@alok gautam Finishing the course isn't what the course was meant for in the first place (except in India, where it's rare to find a good teacher; BTW I'm Indian too)

he teaches in high school

EKGaming i do. His name is mr hernandez. In fact ges more enthusiastic.

alok gautam I think a even balance is good, but some of my teachers are just way too depressing.

I quote.

I've thought about this several times since I've first seen it 11 months ago and have wondered if one does not equal the number but now defines null (i.e. the one is representing something that should be in the space but isn't).

Amazing teacher!You ignited my interest for maths

You have to have real enthusiasm for teaching and want to help students understand and succeed to be a great teacher, and Eddie Woo is definitely one of those. I’m a scientist and although I have to understand maths to some extent, I’m not a maths specialist. I was a became a student again listening to this - and really enjoyed the class!

I've always struggled with maths. Part of me now thinks things could have been different if I'd had an instructor like this.

Great job,that's the kind of teachers that world needs.👍🏻

Very nice introduction to limits. It might be interesting to graph that function.

I can't believe this guy kept me engaged enough to sit through a math class. Props to this man.

This is THE BEST introduction to limits i‘ve EVER seen oh my god! Such an amazing teacher!

Stupid students not giving attention to such an amazing teacher ❤️

so where are these people going to use ZERO TO THE POWER OF ZERO in real life. it's just a waste of time bro.

I wish I had a teacher as passionate as him

Facts. Hate such kind of jerks

I dont believe they mentioned an important part that was overlooked, the m in the exponent of 0^m = 0, m and n are used as whole numbers, so the only possibilities for m or n is integers greater than 0. That is perhaps why he can write both of those and neither is incorrect

Something worth noting is that when you approach zero from the negatives, ie. (-0.000001)^(-0.0000001), we see that x^x approaches -1 instead of 1. So the limit from the right approaches 1, and the limit from the left approaches -1.

Except you can't even get any result for things like e. (-0.000001)^(-0.0000001)... Negative bases cannot be raised to most non-integer exponents. :-B

Exactly. You can concoct any number of other limits x^y where both go to zero. Each time, the result will be different. That's why I think this video doesn't make sense

Omg how good this teacher is. I pressed this video by accident and i watched the whole of it.... I am 28. I am a cook. Don't have to watch this but i like it. If only our teachers would had been so passionate and amazing as this guy.

I started watching this with the understanding that when it got completely over my head I'd bail out and skip to the next video, probably after about a minute and a half. The next time I looked at the progress bar it was at 14 minutes and I felt as though I hadn't even blinked during the presentation. Very well done indeed, Mr. Woo.

Please, save this teacher's DNA so in the future we can start making a copy of him for every high-school math lecture in the world.

@JJ 614 great answer bro

That's right!!! Save his DNA, because as long as we can get Little Jenny Blockbuster to stay awake in pre-algebra, then all those quiet, introspective thinker types can go study the humanities and work at Starbucks. Noether, Turing, Euler, Gauss, I think we can all agree, were never venture capitol material. Think how advanced science could be right now if only someone had scared them off early.

@Rex Robo it isn’t about getting the answer, it’s about critical thinking to deduce the answer. It’s about teaching the students to think for themselves. The question near the end as to why the asymptotic trend toward zero (exponential decay is the phrase the professor used) turned around is an excellent question, and a missed opportunity to say “this tonight’s homework”. It would “grown up” of these student to show a little respect toward the professor and “shut-up” while he is speaking.

No matter how good the teacher is, the main ingredient are always attention and greed to learn, if that's not there no one can teach you.

I have never understood math like this. Thanks sir for giving a new way to learn.

This is the most fasicanting way i've seen someone explain limits. Awesome teacher

This took me back to when i decided to study engineering. These Kind of lessons tought by the correct teacher, make anyone madly in love with maths. Congratulations, now i remembered my passion for this beautiful class.

HI Eddie, thanks for being so through in your teachings. Its easy to follow and learn. A couple of questions, what is i to the power of 0? What does something being raised to the power of 0 even mean, how does something get raised to 0th power?

We can even determine what a complex number in general, to the power of zero is. Given a complex number z in general (where A and B are both real): z = A+B*i Calculate: (A + B*i)^0 Rewrite the value of z in polar form: z = R*e^(i*theta) R = sqrt(A^2 + B^2) theta = arctan2 (A, B) where arctan2 is the 4-quadrant angle resolver function, that takes in both the x and y values in that order, and resolves the angle. z = sqrt(A^2 + B^2) * e^(i*arctan2 (A, B)) Now determine what z^n is equal to, in this form: z=R*e^(i*theta) z^n = R^n * (e^(i*theta)^n Power raised to a power = multiply exponents: (e^(i*theta))^n = e^(i*n*theta) Thus: z^n = R^n*e^(i*n*theta) Plug n=0: z^0 = R^0 * e^(0) z^0 = +1 as long as R does not equal zero, this is valid for all complex numbers. The only time when R would equal zero, is if both A and B are equal to zero, and the given complex number itself is therefore zero.

The short answer is that anything to the zero power, equals 1, as long as the base isn't zero. Since B^1 = B, and B^(n - m) in general equals B^n / B^m, this is how we determine that B^0 = 1 in general. Simply set m=n, and we get B^n/B^n, and any number divided by itself (other than zero) is equal to +1. You can determine what i^0 equals, and it equals +1. When you raise i, the imaginary unit, to integer exponents, you see a repeating pattern that circulates through the complex plane. For i^1, this equals +i, which is points in the positive imaginary direction. For i^2, this equals -1, which points in the negative real direction, 90 degrees CCW from i^1 For i^3, this equals -i, which is 90 deg CCW from i^2 For i^4, this equals +1, which is 90 deg CCW from i^3. And we return to the real axis. We can even apply negative exponents (i.e. reciprocals) to i, and look what we get: i^(-1) = 1/i = 1/i * i/i = i/(i^1) = i/-1 = -i i^(-2) = 1/i^2 = 1/(-1) = -1 i^(-3) = 1/i^3 = 1/(-1*i) = -1*-i = +i i^(-4) = 1/i^4 = 1/1 = +1 In general, where n is any integer, the integer powers of i follow the following pattern: i^(4*n) = +1 i^(4*n + 1) = i i^(4*n + 2) = -1 i^(4*n + 3) = -i And zero is no different. Look at what is exactly between i^1 and i^(-1) in this pattern. i^0 is a case where n=0, and the exponent is a multiple of 4, which makes the answer positive and real. And since the magnitude is 1, the magnitude of the answer is also 1, and we get i^0 = +1.

Eddie: keeps his calculator in a protective case Also Eddie: yeets it onto the table

I totally noticed that too!

Thats what the case is for :P

That is why it has a case :D

@Zenbonzakura I had a better professional opportunity.

Exactly why he can confidently yeet it onto the table😜

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