This is the true message that all teachers should learn: "No matter how uninterested a student is in a topic, if you teach it right, you can make it entertaining to them and help them learn."
For future internet historians: At 1:22 Mr. Woo mentions "People who have spent time on their phones recently know these numbers very well". This is because in 2014 a mobile game called "2048" was all the rage. In that game you slide numbered tiles around to combine like numbered tiles to create larger numbered tiles. The lowest number is 2, so as you can imagine the combinations follow a 2n pattern. Hence 2, 4, 8, 16, etc is quite familiar to young students at the time.
@brotinger_1 That's not a proof. That's just an argument for why it should be defined this way. You need to give a proper definition of a^x before you can prove properties about it.
the slow roar of the classroom realizing at 2:48 to 2:55 must have felt like being an absolute rockstar for teachers. If I would have heard this kind of reaction from the classmates around me, the entire atmosphere could have been different.
Someone explained to me that the reason 0 factorial equals to one is that the idea behind factorial is how many times can a group of data be arranged in different orders. There is only one way to arrange a group of data that has 0 data in it
the problem is: you cant arrange something that doesnt exist. for example what pumpkin did was not arrange nothing in the one and only but he arranged 5 identical boxes. thats an entirely different thing.
@@allorfh2495 the more mathematical explaination is to rearrange the definition formula for factorial. n! = n x (n-1) x (n-2) x (n-3)... x 3 x 2 x 1 = n x (n-1)! So when n=1, 1! = 1 x (1-1)! 1 = 1 x 0! We know 1! Equals to 1, so by algebra, the unknown number 0! = 1
I was a below average student with no interest in math or education until I met someone like this professor in 10th grade teaching geometry. He changed my world and everything. From 10th grade and beyond I was a straight A student graduating with high honors. Some 30 years later I still think of him and how amazing of a teacher he was. There are teachers then teachers like these. You are a gift to many sir.
Their reactions when the explanation came was so relatable. It's one of those Maths things that sounds like it's gonna be so complicated but it boils down to something quite simple and you wonder why you couldnt see it from the start. And this teacher/lecturer/professor would have me getting good grades. He makes me want to learn, and makes it enjoyable and approachable.
I have a teacher like that and holy crap. Everything he teaches me, I almost always get what he's trying to teach me. People always think teaching is easy and everyone can do that. Well yeah but not everyone does it so well like this teacher in the video. I think thats really cool and see it as a gift ✨😊
I like how when he says "people who have spent time on their phones recently knows these numbers VERY WELL" is referring to the 2048 game which was popular at the time
1) I never stopped to think about why n^0=1, I just accepted it. And the way he explained it was super interesting 2) this guy seems like a really cool professor and I would totally love to take his class
I got what you said, it's really frustrating. But look this way: "...because it just is" is a quite more practical and easier way to continue with other topics, sometimes it is just necessary.
Not always the most curious people become teachers and on many places around the world they're usually underpaid. Thank god we now have social networks like TH-cam where we can watch really enthusiastic educators like this one. We as society must spread the world about this sort of content in the web so more people have access to it and more people feel inspired to produce content like this with that same enthusiasm
Literally why i flunked math when we immigrated here in Canada. They over explain the simple stuff, yet when it came to trigo they just tell us to press buttons on the calculator
0:01 Before watching: my answer is because there is only one way or arrange nothing. By not arranging anything. If there are no dishes in the sink how many ways can you do the dishes, one way. By not doing them. Bad example, maybe, but same principle. After watching: I never realized there was a pattern to be followed. That’s freaking cool.
@@dhruvbhagchandani It wasn't my intention to try to get likes, only to speak my mind. And if you're gonna insult someone, at least do it right and write *god's* sake.
You and I have had different teachers. I learned this in middle school when we did probability in algebra. It’s a really simple argument to follow I don’t understand how anyone could be confused by it
@@plazinga See it's exactly that mindset that makes my math teacher unbearable. He thinks that because *he* understands it, everyone else also must, and thus he belittles students when they don't know the answer.
As a teacher, that moment when the students went “Oh!” was so satisfying and empowering. He is clearly a great teacher, teaches with passion and clarity while also being flexible and having a sense of humor
Zero of a certain quantity is equal to zero. pretending wheels are square doesn’t make them square , unless they’re low profile and you turn them 90degrees then look at them from far away (and pretend) .
For last 50 years, I'm one of those who accepted 0! is 1 *but* I now know how! I should try few other various based on those patterns. Nice one Mr.Woo. Thank you!
I find it wholesome that he lets his students breathe, like how a comedian stops talking while the audience is laughing. Some teachers hate those micro feedbacks, such as laughing and murmuring discussions. Nevertheless, both show respect as the students get silent when the teacher starts talking.
Most of my classes were like this at the end and these ones were the best. You just like being there and sometimes tease the teacher while still learning.
a raised to power 0 is one. Thats just how it is Its a rule of exponents. Its a law so shut up and stop disturbing the class Almost every maths teacher
@@gordonramsay5356 It's because people are attracted to the unusual or unintuitive. The weird, etc. Also, they want a quick fix for everything they're interested in, and videos can be highly entertaining to people if they know they'll be no quiz or test on the material. Note that Eddie's seeing the big picture calc video and his quick visual proof for the area of a circle both have over a million views. Learning basic mathematical techniques to solve problems takes work and dedicated practice time something most internet dwellers are definitely not interested in. Hence fewer views there.
My professor explained it in interestingly to me, he said, “the proof comes from trying to figure out how many ways there are to distribute nothing, and it turns out there’s one: you can only give nothing to no one”
@S GALAXY GAMER No,factorials are used in combinations . 3! Means how many ways are there to distribute 3 things to 3 people for ex,and thay is 6.U have 6 combinations on how u can distribute 3 things to 3 people.1! Is only 1 way because u have only one thing and one person.0! U have nothing and no one to give it too,and thats still called a way.U give nothing to no one which makes sense kinda
Hey man, Can u help me? I'm trying to learn english and i can't find a good description about the phrasal verb "Turn out", can u tell me what this mean?
Gabriela Piovesana It’s a little hard to explain but it’s like a way to say something “in the end” like, I thought the roller coaster was scary but it TURNED OUT to be really fun”.
@@Neyobe I get the picture, thanks man, can u help me in just more one thing? I'm trying to find a partner to learn english, by playing some games or just talking. Do you know some site that help me to find someone?
Took me a moment, but when he mentioned that people who have spent time on their phones recently would've seen those numbers, he was talking about 2048. Immediately brought me back to high school when everyone was playing that game in 2014.
Maths is the most beautiful thing that ever happened in this world and to have representatives like him who really love what they do, now that's beautiful.❤
Nothing better than finding a professional who love/care for his job. I HATE history, because all teachers only cares about dates and names. Nothing else. I once had a substitute historian teacher, for like 3 months, and she would talk about the time period like she was a time traveler, explaining how the society worked back then, politics, religion, etc. It was the best. So after that i realized there's no bad disciplines, only bad teachers. The reason for the latter varies, as we all know...
It’s not always up to the teachers though, you have to remember they are part of a much larger system. There are certain standards and checkpoints that have to be met in order to satisfy the state or district. This results in the bullet point learning you hate. Your substitute isn’t beholden to this because they’re just a placeholder, so they have more freedom to teach. It’s a sad state of affairs but one more complicated than teachers being shit.
One of my history teachers didn't care much about dates and names. His focus was mostly on the "why". His class turned out to be one of the most challenging classes in my EEE degree.
@@yohithere6306 EEE=Eelectrical & electronics engineering? If it is, then Wow!!! It is amazing for EEE undergraduate students in your country to study history as a compulsory subject.
I had a geography teacher who had traveled the world many times over. All his slides for notes he would use his own photos he had taken and give actual first hand knowledge about the place he had been. It was honestly so cool.
I love when they can explain a origin of things, and hate it when they tell me to remember the result because it should like that, it is superfluous to explain for a thing*blame blame blame*. I search for some of the explanations, feel I can remember better for my knowledge
Bruh seriously! Makes me wonder what kinda class hes teaching. Like if you already have "3! = 6" then just multiply the product of that by 4.. didnt e en hear the right answer called out 😂
And my teacher was like 2 + 2 = 4 Now you can do it by yourself, a home work for you :- Michael has 4 apples, his train is 7 minutes late, calculate the mass of the sun.
I won't blame him, powers are hard to calculate under 1 or 2 seconds unless you memorize them perfectly. He probably made a mistake judging by such a short time he had.
someone imagined this "2×3" instead of this "2^3" in his mind quite normal mistake when brain isnt fully active and have to respond quickly (like rapid fire round coz both involved multiplication and same numbers edit: also 2×3 is simple than 2^3 and our brain have fundamental nature to choose easy way requires less effort..
Since I see so many other people telling personal stories, I'll add mine to the pot. Eddie reminds me of my current AP Calculus teacher, whom also taught my Precalculus class last year. Now, up until Precalculus, I didn't really care too much about math. I was always pretty good at math, but it wasn't something I really thought much of. It was just another subject in school to me. This mindset changed when I took his class. This Precalculus class (which I took at the same time as my school's Algebra 2 class) scratched an itch that I didn't know I had in my brain. Not only were we learning things as well as why and how they work (which was a first for me), but my teacher also knew where the concepts we were learning got applied. Whenever I'd ask him where the subject we were learning was used, he would say something like "Oh, this stuff is used to calculate the shape of Formula 1 cars". In just that one year, I went from being indifferent to math to actually liking it quite a bit. Fast forward to now and I am completely in love with math. Although calc can be hard, there's just something about that is so... satisfying. And my teacher has kept his trend of giving examples of where things are applied whenever asked. This comment is to you, Mr. Kramer. Thank you so very much for igniting a passion that I didn't know I had
As an educator for the past 20 years, yes, there is a sort of satisfaction with getting this sort of reaction from a class. It demonstrates engagement; But what's infinitely more satisfying is (assuming you have their complete attention and all in the same page) when you get them to truly contemplate a completely new or groundbreaking idea; something that challenges their existing notions and understanding. Even better, If you get them to start asking additional questions to process that idea, and they start asking those questions not just to you as the teacher or facilitator, but to each other in class, and then it ricochets back and forth between you and the rest of the class, those are truly the moments that make teaching satisfying, IMHO.
@@jcnbw01 could you please tell us about a time this happened if you can recall (edit: just out of curiosity, i've never been in a class like this and I kinda want to know more)
its kinda crazy because as a math student, you never are taught WHY things are the way they are, teachers really just tell us to accept it because that is the way math works. Even i was kinda in awe seeing this because i was never taught this in math. UPDATE: Im currently taking calculus 2 in college, and this topic came up during class since we were covering root/ratio test, which deals with factorials. Even my calc professor didn't know exactly why 0! is 1 and I explained to her from this video!
actually your teacher's explanation is kinda same with this guy. you still dont have a sensible reason why 2⁰=1. you know its 1 cuz it has to be 1 for the rules on the other numbers. But you cant prove why 2⁰=1 is. Its exactly because thats the way math works. we better accept it as 1. you to better understand, let me give an example. 0⁰ is sometimes undefined sometimes it equals 1. we define it as 1 cuz it makes the things easier. we sometimes accept it as undefine cuz if we define it we make mistakes. In algebra its accepted as 1 and in analysis accepted as undefined. so its about us. not exactly cuz of the rule pattern.
Ya education isn't imagination anymore its memorization now. Its not our fault though our system did this. See our ancestors did all the imagination and now we have just to memorize their works. Life is easy but boring at the same time.
2:50 -> The sound of having the most fantastic experience in a learning situation by having a teacher, who truly understands how to explain in a way that it sticks. Aha-moments are the ones that stick to your brain. I seriously just watched this video again, just to hear this again.
Lol I love how engineers and mathematicians see the world so differently. Mathmeticians appreciate the intricacies of numbers for what they are and all of their complexity. Engineers appreciate numbers for what they can do for them despite their complexity.
Mathematics, as a discipline, is one of the various conceptual worlds. It resides in the minds of people. Language enables sharing and discussing mathematics, so it becomes ever refined. But the primary source of mathematical ideas is the physical universe, for its natural laws are constrained by mathematics, not the discipline but the underlying pattern or subset of the whole of idealized relationships, known or unknown. An example of a primary source of mathematics: Natural numbers relate to collections of individual objects, they are the collections' cardinals. An example of a non-physical application of mathematics: five mathematical theorems, three dreams, eight contradictions, four myths. Engineers constantly deal with the physical world, it's their job. For them, the relationships between mathematics and its primary source, the real world, is fundamental. Mathematicians constantly deal with the discipline of mathematics, of course. They try to squeeze the most of what they best know, and so, mathematics expands. Philosophers also appreciate mathematics. Bertrand Russell's paradox of "the sets that do not contain themselves...." is an example. Artists and mathematics? Of course! Tilings are an example. Fractals, another. So, who do not love mathematics? Those who heard that mathematics was something hard, ugly and unworthy of trying. Those who prefer sports to thinking. And so on.... My daughter is 35. I have been teaching her mathematics for a whole year, for she asked me to. She was not too comfortable with what she had been taught at school two decades earlier. She takes free time for mathematics whenever she can, even though she has to work hard most of the day for a living. I am very proud of her.
@@wafikiri_ There is yet another subset of people who hate mathematics, although unintentionally; those who were never taught about the underlying pattern because their teachers were unwilling or unable to explain the context of the lesson and simply told them to copy the formulas. I wish I had a teacher like this who could explain how mathematics can be a creative pursuit rather than just rote memorization.
In college you get to choose which professors class you sign up for. If you're smart you figure out which ones are bad and avoid them. Once you're taking 300 level classes TRY TO FIND ONE THAT USES ENGLISH AS A FIRST LANGUAGE. try.
Kuba Marcin actually not he’s young teacher, but his chacteristic is tolerant ( in doubt), my teacher is more double aged than him and he still cool like him, but in some aspect you need some someone have calmness and expiriences, i’m not wanna judge him that his self - easteem quite high by first look, but I used to meet a similar guy like him, hence his positive out side while inside he feel very conflicted with students as same level as him ( sr for my bad english explanation )
I disagree entirely. 1! is 1, and you're saying 0! is also 1. Basically 1!=0! So you can cancel the ! from both sides and you're saying 1=0. 1 does not equal 0.
@@jazzabighits4473 No, you can't just cancel ! from both sides. Factorial is a complex function and ! is just shorthand for it, it doesn't work that way.
As a US math teacher who has given that career up: if all students, or even 1/2 of all students, were this engaged and respectful (hell, if their fucking parents were even) then maybe you'd have teachers like this in the states. Poverty culture enforces poverty is what I'll leave you with.
I love his lesson at the end about Fourier! Those kids are lucky to have such a passionate math teacher. You can just feel his enthusiasm and passion for it when he was giving that explanation.
I asked my maths teacher how is a^0=1. He said me in the following way. a^0= a^(1-1)=(a^1)*(a^-1)=(a^1)/(a^1) =a/a=1. Note: "a" is any non-zero number.
@@allin1club413 Ah, thank you! I've assumed that 'a' would be a variable, but I didn't get that a1 is supposed to mean a^1. I thought you meant a*1, since you don't have to write the multiplication sign (although the number should have been first if that was the case), but then the lower part wouldn't make any sense, so I assumed that 'a' would be something else. To summarize: I understand it now, thank you!
@2:00 I was thinking the following way instead: 2^2 = 4. 2^-2 = 1/4. Then, say, we multiply those two. (2^2) * (2^-2) = 4 * 1/4 = 1. Now, we know (2^2) * (2^-2) can also be written as 2^(2-2). That would then make 2^0 = 1.
I used to say the same thing, and I ended up becoming a math teacher. I'm very similar to him by showing why things are, energetic, and breaking things down to simple levels. In my classes I have students that have gotten D's and F's in math for the last few years saying they've never understood math so much and about half the class say math has never come so easy. Despite that, there are also many kids that prefer to just zone out, not take notes, not attempt any work, prefer to try get on their phones, or try to just do anything other than math. All these kids say it's super hard... Anyway, my point is no matter how great the math teacher is, there are always students that will ignore instruction.
One more way of understanding this is- n ! is basically the arrangement of n different object in n spaces. Now, logically an empty set can be ordered in 1 way only, hence 0!=1.
It's to do with probability and the number of outcomes something has. e.g. you arrange 10 differently coloured umbrellas on 10 hooks and you must use every single umbrella you have (idk why I chose umbrellas but just run with me on this one), there are 10! different possible arrangements that you could have - since an umbrella cannot be chosen again once it is placed. The same is true for 0 umbrellas where there is 0! possible combinations which equals 1 (empty hooks can count as a possibility here since it technically fits the criteria of all umbrellas being "used").
He is really a very great, interactive & a very patient teacher. Every word he speaks is to the point. I have seen a very few teachers who have really contributed their life in this teaching field & enjoys their profession.
For the a^0 i always had it explained to me as 1 * a^ any power = a^ that power So like we had the list of powers, like 2^5 2^4 2^3 2^2 2^1 2^0 and then we added a *1 at the end of all of them. So we take 2^0 as 2 being multiplied by itself 0 times, so it is just not there, so the only result left is 1
That's perfect. I would say this is a better definition of powers. Instead of saying a^b is a multiplied by itself b times (when there are only b-1 multiplications. Like 2^3 = 2*2*2. Here there are only 2 multiplication symbols and hence 2 multiplications going on. 1st multiplication: 2*2=4, 2nd multiplication: 4*2=8). . A better definition would be a^b is 1 multiplied with "a", b number of times. So 2^3 = 1*2*2*2 2^2 = 1*2*2 2^1 = 1*2 2^0 = 1 (we muliply it with 2, 0 times. That means we don't multiply it with 2 at all. So it's still 1)
I searched cause i had factorials explained as the amount of ways you can arrange something and i was wondering how can you even arrange 0 of something in 1 way? Wouldn’t it be that theres 0 ways to arrange 0 things?
Correct explaination for 0!=1 is As we know n!=n(n-1)! If we put n=1 here 1!=1(1-1)! This will be equal to 1!=1*0! so 0!=1 I hope this method is clear to everyone😃
we can consider a case where we have to select 0 objects out of n objects (unidentical) practically the answer will be 1 but formulated answer will be nC0 which will be n!/0!(n-0)! = No. of ways of selection of 0 object from n objects practically RHS = 1 therefore, n!/0!*n! = 1 given that 1/ 0! = 1 therefore 0! = 1
I dropped out of Engineering in my last year and chose Real Estate as a profession, because I sucked at Maths, especially Fourier stuffs and Intergrations. I would never understand them. But now after 10 years, as im reaching 30s.....Im watching many Maths and Physics videos on TH-cam and Im understanding everything. I just wish I had teachers like him!
You can see the passion in this man's voice, the way he conducts himself, and the way he explains and projects his thoughts like this man really loves doing what he does, rather than spitting knowledge and expecting students to regurgitate without the students thinking, he makes the students think as he shows the magic and how fascinating math is theoretically. I always loved teachers like that where they truly enjoy doing what they do. They are what makes learning in school so fun and those are the teachers I hold the upmost highest respect for.
When I did it in this way, many pupils were more than sceptical and just wanted to memorize blindly. And because the majority is silent, the loud losers and their very "protective" parents dictate the school what to do and how to do it.
YES! And the way he explain that just messing around with numbers and logic can be so fucking important for future needs beyond our understanding makes ME want to learn math! And i fucking hated this shit through high school. This teacher is basically saying: Learn stuff to just mess around with it, you may just discorver something
I have utmost respect for John Gabriel the author of New Calculus channel on youtube, he has discovered and shared the most remarkable things in mathematics which I had the chance to encounter so far
'The point is that it doesn't matter if it can be used for something, it's that it has a consistent set of rules that is meaningful' see how every other teacher replies 'you have to learn it because it's on the spec' or 'you just have to know it', this is a much better way of saying pretty much the same thing.
Weird how I read your comment the exact time he said that. My past math teacher is great at her field, but she's too fast and she tends to story tell my seatmates don't know what we're talking about anymore.
if you do programming it is useful... e.g. implementing a fold operation with multiplication operator. If you know 0! = 1, you will use the correct identity value :) As a programmer, the 'pure' maths is more useful than 'applied' maths, the names are misleading.
William Yep! And if you do probability, for example, if you start studying for the actuarial exams, you will need to use 0! in the formula for combinations: n choose r formula - as n choose 0; as well as permutations: n P r, as in n P 0. That is the only way that combinatorics and their use for probability makes sense.
Trying to imagine how my life might be different if I had just ONE math teacher who taught with this energy and cared this much about me understanding math.
I am learning math the hard way at university after years of total lack of knowledge. I have been on the edge of crying so many times. The fact that I can understand this lecture is already a victory to me.
You realize it's not just maths. It's pretty much anything. It really boils down to nurture. If you have a really good mentor who knows his shit and also knows how to convey that to you. Bonus! That's where luck plays in. Everyone has potential but it requires the right person to bring that out of you. Sure you can say why not do it by yourself? Trust me you can't. Some things you have to do it with others. It's also the reason why we humans are social beings. I don't want to bring psychology and philosophy. Coz I can go all day.
Here is an another reason why a^0 = 1. According to the law of exponents: (a^m)/(a^n) = a^(m-n) Let's take any number raised to any power. Let us take a^x. Now let a^x = y Then, y/y = 1 a^x/a^x = 1 According to law of exponents a^(x-x) =1 a^0 = 1
I think one of his most overlooked skills is letting his class talk to each other. At first I was annoyed by their noise but if you pay attention to them they get excited when new info is being presented, they are sharing their epiphanies and genuine interest
He also stops to look around with a smile, he is often seeing how he can interact with them if he overhears a student staying on topic and talking about the subject
i think he stops bc students use the cover of the noise made by the teacher to have their own conversations. When he is silent its easy to spot whos being loud source: im a student who does this sometimes
Not always, when there is interest it's ok, but it's horrible when it's just an irresponsible group. The teacher should always have the authority to shut them up. But obviously this video is a totally different situation. Was wholesome hearing their reactions
This is excellent teaching. Here I was expecting him to pull out some obscure logical lemma some mathematician made three centuries ago to account for some edge case for where 0! not equalling 0 creates some kind of contradiction, but it’s just... the pattern continues. A number divided by itself is always 1. Damn. I can’t believe I hadn’t given this thought before. EDIT: YES I GET IT ZERO IS A SPECIAL CASE STILL. The pattern only continues because the rest of the factorials exist in the domain of the positive natural numbers. I swear some of you would freak out at "a prime number is a number that can only be divided by itself and one" if I didn't also say "except for 1". It's almost as if special cases have reasons for existing that aren't entirely self-consistent, but are important for mathematical patterns to continue in a logical fashion.
@@OtherDAS Not necessarily. In another video he explains dividing by zero. And He explains that division is just repeated subtraction (just as multiplication is just repeated addition) until you reach 0. If you subtract zero from zero you are already at zero. Of course you can argue that you can subtract it zero times, because you're already at zero before you subtract even once. But if you don't subtract at all, because you are already at zero, you're not dividing (repeated subtracting) at all and therefore by definition not dividing anything.
He didn’t even give the complete reasoning for a^0 😂 It’s because (for example) a^2 / a^2 is clearly 1 because it’s a number divided by itself, but you could also simplify it by subtracting the exponents because they have the same base (a), so a^2 / a^2 can also be written as a^0, which is 1 It’s more than just continuing a pattern because we have no reason to believe we shouldn’t, there’s an actual mathematical explanation
The way he commands the respect of his class to all shut up and let him finish is amazing. It goes to show that a good teacher who is passionate about his material is unbeatable when they start explaining *why* they are so passionate.
So, a practical explanation: Factorial is an operation that says in how many different ways you can sort a determinate amount of options. So let's just change "options" for "cubes". In how many ways can i sort my 6 cubes? 6! or 720 In how many ways can i sort my 5 cubes? 5! or 120 In how many ways can i sort my 4 cubes? 4! or 24 In how many ways can i sort my 3 cubes? 3! or 6 In how many ways can i sort my 2 cubes? 2! or 2 In how many ways can i sort my 1 cubes? 1! or 1 In how many ways can i sort my 0 cubes? There is only one way of "having no cubes", so 0! must be 1
This is a more correct way to explain 0! than the video explanation. I mean, that's fine, but this is better because it doesn't use the definition of n! as "the product of every positive integer equal or smaller than n" and then finds a way around it. Another cool way to explain 0! is by introducing Euler's Gamma function, which also gives you values for any real number's factorial except for negative integers.
Instead of being forced, if our curiosity is engaged, why'd anyone not learn things? This allows us to study what we desire and choose to. And we can learn other subjects without having to give exams for them while focusing on the subjects that we want to excel in.
I can't believe I'm watching this video for entertainment
This is the true message that all teachers should learn:
"No matter how uninterested a student is in a topic, if you teach it right, you can make it entertaining to them and help them learn."
@bax warrior me neither
@@amadodiallo3167 Absolutely, I got a teacher that has been able to make boring even n-dimentional curves
Same
*m u s t o b e y r e c o m m e n d a t i o n s*
For future internet historians:
At 1:22 Mr. Woo mentions "People who have spent time on their phones recently know these numbers very well". This is because in 2014 a mobile game called "2048" was all the rage. In that game you slide numbered tiles around to combine like numbered tiles to create larger numbered tiles. The lowest number is 2, so as you can imagine the combinations follow a 2n pattern. Hence 2, 4, 8, 16, etc is quite familiar to young students at the time.
oh gawd, I've kinda forgotten about that game.
lmaoooo
chad
@@ryanregis99 h ky h jb jb j+j-hy hj+j+just hub+b
damn i'm a high schooler right now and 2048 is still all the rage where i'm at, guess we're stuck in the past
Wish I’d had this guy as a maths teacher all those years ago. The “why” is so important to assist understanding…..we just got taught the “how”.
Absolutely crt...!
@brotinger_1 we got taught exactly that in my school
@brotinger_1 That's not a proof. That's just an argument for why it should be defined this way. You need to give a proper definition of a^x before you can prove properties about it.
@brotinger_1 p... P. . Mm mm mm. Mm mm. O all o!o. Mmg, mm mm mm mm mm me mom o miss. O MMO o mm l mm mm mm. momma .p
Mm
Mm moo o
Exactly
the slow roar of the classroom realizing at 2:48 to 2:55 must have felt like being an absolute rockstar for teachers. If I would have heard this kind of reaction from the classmates around me, the entire atmosphere could have been different.
having an engaging teacher makes all the difference
@@ognam1exactly
He is a rockstar❤❤
🎉🎉🎉
@@ognam1❤❤❤❤
Someone explained to me that the reason 0 factorial equals to one is that the idea behind factorial is how many times can a group of data be arranged in different orders. There is only one way to arrange a group of data that has 0 data in it
That makes a lot more sense for the concept. If you can have nothing in 5 boxes (0•5). Then those boxes are also organized the same.
the problem is: you cant arrange something that doesnt exist. for example what pumpkin did was not arrange nothing in the one and only but he arranged 5 identical boxes. thats an entirely different thing.
@@allorfh2495 it's a thing of probability. Being unable to arrange it counts as a possible outcome, so it's 1.
@@allorfh2495 the more mathematical explaination is to rearrange the definition formula for factorial.
n! = n x (n-1) x (n-2) x (n-3)... x 3 x 2 x 1
= n x (n-1)!
So when n=1,
1! = 1 x (1-1)!
1 = 1 x 0!
We know 1! Equals to 1, so by algebra, the unknown number 0! = 1
@@yuewingman456 but isnt factorial outcome a value (of any number) instead of probability?
Why isn’t every math teacher like him;(
My teacher isn't like this but she is amazing
If all teachers were like this one, people still complain.
My teacher is exactly like this, but much older and speaks Dutch
You have to be good when you're uploading it on TH-cam Lmao
bcz if every math teacher would be like him then no would have interest in his channel
but seriously he is a great teacher
I was a below average student with no interest in math or education until I met someone like this professor in 10th grade teaching geometry. He changed my world and everything. From 10th grade and beyond I was a straight A student graduating with high honors. Some 30 years later I still think of him and how amazing of a teacher he was. There are teachers then teachers like these. You are a gift to many sir.
These are the stories you love to hear. Thank you for sharing.
Oh my god, I have a teacher in 10th grade Geometry too and he really sparked that math passion in me again.
Some thirty years later
What do you mean by this???
What his present age is??
@@rajeshkumarKona-pt2zk They mean that they still remember how good their math professor was, even though it's been 30 years.
..... a good teacher changes destinies...
Their reactions when the explanation came was so relatable. It's one of those Maths things that sounds like it's gonna be so complicated but it boils down to something quite simple and you wonder why you couldnt see it from the start.
And this teacher/lecturer/professor would have me getting good grades. He makes me want to learn, and makes it enjoyable and approachable.
This is exactly what a teacher is supposed to do for students: create curiosity towards the subject.
I have a teacher like that and holy crap. Everything he teaches me, I almost always get what he's trying to teach me. People always think teaching is easy and everyone can do that. Well yeah but not everyone does it so well like this teacher in the video. I think thats really cool and see it as a gift ✨😊
the students wont stfu, is that how it is these days?
I pretty sure he's the no.1 math teacher in Australia
@@akira-chan591 you right. Our education system is itself just a big crap
@@headhumper3398 yep that basically most of the lectures nowadays
I like how when he says "people who have spent time on their phones recently knows these numbers VERY WELL" is referring to the 2048 game which was popular at the time
ohh good catch I completly forgot about that game.
When I heard it this reference i was like was it actually 7 years ago
thought it was about their test grades lol
@@remikarim562 I was ten and playing it at the time so no excuses for me
Oh I thought it was talking about how the storage for phones is a result of a power of two.
1) I never stopped to think about why n^0=1, I just accepted it. And the way he explained it was super interesting
2) this guy seems like a really cool professor and I would totally love to take his class
@brotinger_1 wow. Thats cool as well
@brotinger_1 this is the correct proof in math class. But I don't think normal students would grasp this better.
@brotinger_1 but can you stop spamming doe
@@arzaseb ???
i rmb my teacher gave me another explanation which is also very make sense, but now i get to know another interesting explanation haha
I love how engaged the class is! It really makes learning so much better.
How many people have asked their teachers and were told “...because it just is”
Literally. So frustrating.
I got what you said, it's really frustrating. But look this way: "...because it just is" is a quite more practical and easier way to continue with other topics, sometimes it is just necessary.
Not always the most curious people become teachers and on many places around the world they're usually underpaid. Thank god we now have social networks like TH-cam where we can watch really enthusiastic educators like this one. We as society must spread the world about this sort of content in the web so more people have access to it and more people feel inspired to produce content like this with that same enthusiasm
I got so used to that so when I met this I figured it out myself.
Literally why i flunked math when we immigrated here in Canada. They over explain the simple stuff, yet when it came to trigo they just tell us to press buttons on the calculator
Teacher: "and i divided by one"
Class: "WOOAHHHH!"
I'd do the same there
@@mrp0001 same. Lol I do that all the time because maths is always so exciting
Oh my god, he divided by one.
Every teacher's favourite sound.
I laughed out loud when I watched this part. :D
This man actually makes me want to have math class. Mad respect.
With him at least
datgamerian yea, I have had previous few teachers as engaging as this. It’s just Plowing through lesson after lesson for me...
i hope so i have that kind od teacher in math class simply the best
I was fortunate enough to have a math/science teacher like this. A good teacher really makes all the difference.
This feeling apply when he teaches when you solves it yourself you got frustrated.
0:01
Before watching: my answer is because there is only one way or arrange nothing. By not arranging anything.
If there are no dishes in the sink how many ways can you do the dishes, one way. By not doing them. Bad example, maybe, but same principle.
After watching: I never realized there was a pattern to be followed. That’s freaking cool.
Meanwhile my math teacher is: "That's just the way it is. Don't question it!"
Which usually means they don't know the answer either, they only know how to regurgitate what they've learned.
@@dhruvbhagchandani It wasn't my intention to try to get likes, only to speak my mind. And if you're gonna insult someone, at least do it right and write *god's* sake.
You and I have had different teachers. I learned this in middle school when we did probability in algebra. It’s a really simple argument to follow I don’t understand how anyone could be confused by it
@@plazinga See it's exactly that mindset that makes my math teacher unbearable. He thinks that because *he* understands it, everyone else also must, and thus he belittles students when they don't know the answer.
**STOLEN COMMENT ALERT**
Someone who clearly loves his job. Thank god there are people like this in teaching.
❤❤❤
🎉🎉🎉🎉🎉🎉🎉
This was 10 years ago 😭
@@sadhikarora6540 we already know it ikr👏👏👏lmfao😂😂😂
@@sadhikarora6540 whatevereh👻👻😎😎
As a teacher, that moment when the students went “Oh!” was so satisfying and empowering. He is clearly a great teacher, teaches with passion and clarity while also being flexible and having a sense of humor
I'M SMART BECAUSE I USE TH-cam. I'M GOING TO RAISE MY KIDS TO NEVER GO TO SCHOOL. EVERYTHING CAN BE LEARNED ON TH-cam.
@@CooManTunes ok
Jesus, my guy coo is having so some sort of revolution
Zero of a certain quantity is equal to zero. pretending wheels are square doesn’t make them square , unless they’re low profile and you turn them 90degrees then look at them from far away (and pretend) .
@@CooManTunes cool
For last 50 years, I'm one of those who accepted 0! is 1 *but* I now know how! I should try few other various based on those patterns. Nice one Mr.Woo. Thank you!
I find it wholesome that he lets his students breathe, like how a comedian stops talking while the audience is laughing. Some teachers hate those micro feedbacks, such as laughing and murmuring discussions. Nevertheless, both show respect as the students get silent when the teacher starts talking.
Most of my classes were like this at the end and these ones were the best. You just like being there and sometimes tease the teacher while still learning.
Ur depressed
Basically an educational standup
@Repent and believe in Jesus Christ shut up
I'M SMART BECAUSE I USE TH-cam. I'M GOING TO RAISE MY KIDS TO NEVER GO TO SCHOOL. EVERYTHING CAN BE LEARNED ON TH-cam.
Wow math is actually interesting when someone knows how to explain it well
Shi kha 😂
How to roast all math teachers with 1 sentence
You can say that to almost all subjects actually.
@@vectrom21 teachers sucks already
a raised to power 0 is one. Thats just how it is
Its a rule of exponents. Its a law so shut up and stop disturbing the class
Almost every maths teacher
Love how everyone's complimenting him and wishes he was their maths teacher when he still makes normal videos (lessons) and hardly gets any views
Yeah not every math lesson can be like this or you learn nothing
Thousands of views counts "barely" to you?0
@@dank_lord no but when you compare it to the amount of views that this video accumulated, its quite small.
@@gordonramsay5356 It's because people are attracted to the unusual or unintuitive. The weird, etc. Also, they want a quick fix for everything they're interested in, and videos can be highly entertaining to people if they know they'll be no quiz or test on the material. Note that Eddie's seeing the big picture calc video and his quick visual proof for the area of a circle both have over a million views. Learning basic mathematical techniques to solve problems takes work and dedicated practice time something most internet dwellers are definitely not interested in. Hence fewer views there.
I watch them even though they’re like what, 5 years advanced
Who is watching this after 10 years in 2024 😂
😂
😂
😂
"Maths can be used to do stuff and that's nice..."
-This Guy, possibly the coolest math teacher on earth
Eddie Woo
@@lakshaykumarwalia4163 Eddie who?
Woo is his last name
@@lakshaykumarwalia4163 Who is his last name?
Right 👍👍👌
The most mysterious things in the Universe*
1- Black-holes
2- Bermuda triangle
3- TH-cam algorithm
Rain Flop but people have made black holes on earth
BBC Crawling *universe
Dominator Death87 but there are none currently existing
@Rain Flop You didn't have to comment just enjoy the joke :L
@Rain Flop he said world.not earth. World is bigger than our universe
My professor explained it in interestingly to me, he said, “the proof comes from trying to figure out how many ways there are to distribute nothing, and it turns out there’s one: you can only give nothing to no one”
That's an interesting approach and that is what makes maths fascinating! Because there's a lot of ways to come to the same conclusion
This way seems to be through PnC
Exactly same thing was explained to me by my teacher.... And that is the best logical...
@S GALAXY GAMER No,factorials are used in combinations . 3! Means how many ways are there to distribute 3 things to 3 people for ex,and thay is 6.U have 6 combinations on how u can distribute 3 things to 3 people.1! Is only 1 way because u have only one thing and one person.0! U have nothing and no one to give it too,and thats still called a way.U give nothing to no one which makes sense kinda
very well explained, thanks. So there is only 1 way of arranging 0 marbles in a line. So 0!=1. Beautiful explanation, thanks.
You can also explain a^0=1 like this:
aⁿ/aⁿ=aⁿ⁻ⁿ => 1=a⁰
Brilliant
ikr that's what I was thinking
*I think I gained brain cells while watching this.*
Me too. I used to be dumb before.
@@rachitanayak_ 😂😂😭😭RIP the old you
I think I lost a brain cell reading this comment
@@ISGNN ការ
@@charlestalks5638 👩🔧
This guy is so smart he may explain youtube's algorithm that got us here
Hahahaha pzlzz request him i wanna know it.
Underrated comment!
Blue shirt
Facts lol
@@besikothabolbina5447 Lmao
this is the most engaged I've seen a math class in my whole life. lmao.
I know! It was almost like a town hall meeting
Math is great especially when you have a fun teacher :D
you havent seen many, then
fr its unbelievable
I think you wanted to say "engaging
2:50 love that sudden realization from the students
I think all people want a teacher like him
I know I did growing up
And some want to be a teacher like him😋
This turned out to be way cooler than I had imagined.
His class usually does
Same
Hey man, Can u help me? I'm trying to learn english and i can't find a good description about the phrasal verb "Turn out", can u tell me what this mean?
Gabriela Piovesana
It’s a little hard to explain but it’s like a way to say something “in the end” like, I thought the roller coaster was scary but it TURNED OUT to be really fun”.
@@Neyobe I get the picture, thanks man, can u help me in just more one thing? I'm trying to find a partner to learn english, by playing some games or just talking. Do you know some site that help me to find someone?
Wow, a teacher who actually *teaches*
JD actually, the fonction and the Fourier proposition, works with function that repeat, so it’s quite false
Whoooosh
@@Nath_here_is_music no. Just change Fourier infinite sum to Fourier integral
With a class who is actually interested!
They are called "educators" :)
Cheers mate this is a top quality video to watch on my Friday night because I am an individual full of life.
Me: why is 0!=1 ?
My teacher: just accept it and don't think about it.
What about the reality where Hitler cured cancer? The answer is don't think about it.
Its a definition , this vid is not proof
same here
It's called an axiom this is something admit without having to prove it
Lol
I watched “Proof 1 = 2.” And now I am getting recommended math
Same here
Same here too
Same video I watched and I m too getting recommends maths.
Same
Can't like it is at 69 likes
Took me a moment, but when he mentioned that people who have spent time on their phones recently would've seen those numbers, he was talking about 2048. Immediately brought me back to high school when everyone was playing that game in 2014.
th-cam.com/video/wtbcaWnybzs/w-d-xo.html
Damn, i miss that game hahahaha
@@MrZoolook same XD
Which game
@@bait5257 2048
Maths is the most beautiful thing that ever happened in this world and to have representatives like him who really love what they do, now that's beautiful.❤
Albert Einstein - "If you can't explain it simply, you don't understand it well enough."
Or you don't have the vocabulary
Max S wasn't it Feynman?
“You can make-up any quote on the internet using this format” -Abraham Lincoln
@@FFeras and he used the reverse format, name at beginning and quote after that
It is said that Einstein wasn't a good teacher.
Nothing better than finding a professional who love/care for his job.
I HATE history, because all teachers only cares about dates and names. Nothing else.
I once had a substitute historian teacher, for like 3 months, and she would talk about the time period like she was a time traveler, explaining how the society worked back then, politics, religion, etc.
It was the best.
So after that i realized there's no bad disciplines, only bad teachers.
The reason for the latter varies, as we all know...
It’s not always up to the teachers though, you have to remember they are part of a much larger system. There are certain standards and checkpoints that have to be met in order to satisfy the state or district. This results in the bullet point learning you hate. Your substitute isn’t beholden to this because they’re just a placeholder, so they have more freedom to teach. It’s a sad state of affairs but one more complicated than teachers being shit.
Exactly! I agree with you, especially with the last para
One of my history teachers didn't care much about dates and names. His focus was mostly on the "why". His class turned out to be one of the most challenging classes in my EEE degree.
@@yohithere6306 EEE=Eelectrical & electronics engineering? If it is, then Wow!!! It is amazing for EEE undergraduate students in your country to study history as a compulsory subject.
I had a geography teacher who had traveled the world many times over. All his slides for notes he would use his own photos he had taken and give actual first hand knowledge about the place he had been. It was honestly so cool.
This teacher: *explains why a0 = 1*
My teacher: "It's 1, that's the way it is, just remember it"
I love when they can explain a origin of things, and hate it when they tell me to remember the result because it should like that, it is superfluous to explain for a thing*blame blame blame*. I search for some of the explanations, feel I can remember better for my knowledge
and my teacher replied because a^(x-y)=a^x/a^y...now let x=y then a^(y-y)=a^y/a^y then a^0=1
🤣🤣
Indian teacher for sure
@@muhammednibeen2268 Indian teachers teach the way Rajat Pratap has said. a^0= a^(t-t) = a^t/a^t= 1.
man if only i had a maths teacher like you, i would have excelled
2:50
Math teacher: 1/1 = 1
Everyone in the class: (Loses their mind)
If you dont understand then shut up
Autism Prevailed in class
.
@@dennissantiago4524 yup it's soo hard to understand 1/1.
@@culturedvulture2015 take a look at the process you dumbass
I’m on Christmas break I chose to watch this video willingly
Same :) Albeit I’m stuck in bed due to a surgery, but I could’ve watched something else.
I wish you a good recovery friend 🙂
Me too. It sucks more because this actually taught me some math I was doing in class before break
This isnt even the first time ive watched this and i chose it for fun
@@erikhjortsater5461 feel better mate
TH-cam: *”It’s okay, they’ll watch anything during quarantine”*
Jokes on youtube I actually like math facts
Jokes on TH-cam I was curious
well do you regret it ? because I, don't 😁
But it was fabulous 😍
Jokes on youtube, whatever this is, is beautiful and a piece of art.
This dude knows his shit. I love teachers who make normally boring subjects fun like this
“4 factorial ?”
someone in the background : eighttt
I would have said that
@@joannot6706 Same lmao
Backbencher said that
LMAO.........
Bruh seriously! Makes me wonder what kinda class hes teaching. Like if you already have "3! = 6" then just multiply the product of that by 4.. didnt e en hear the right answer called out 😂
And my teacher was like
2 + 2 = 4
Now you can do it by yourself, a home work for you :- Michael has 4 apples, his train is 7 minutes late, calculate the mass of the sun.
SO UNDERATED COMMENT OMG LMAO
Omg 😂😂 better truth 😂😂 xD haha
nice try bro too much corny
So true 😔
I mean, i would like to get that as homework since you can just search thr answer on google
2 cubed
someone in the background: 6
I was looking for this comment 😁😁😁
I won't blame him, powers are hard to calculate under 1 or 2 seconds unless you memorize them perfectly. He probably made a mistake judging by such a short time he had.
@@ansh6370 dude we are talking about 2 cubed 😂😂😂
someone imagined this "2×3" instead of this "2^3" in his mind
quite normal mistake when brain isnt fully active and have to respond quickly (like rapid fire round coz both involved multiplication and same numbers
edit: also 2×3 is simple than 2^3 and our brain have fundamental nature to choose easy way requires less effort..
@@ansh6370 lol😂
Since I see so many other people telling personal stories, I'll add mine to the pot.
Eddie reminds me of my current AP Calculus teacher, whom also taught my Precalculus class last year. Now, up until Precalculus, I didn't really care too much about math. I was always pretty good at math, but it wasn't something I really thought much of. It was just another subject in school to me. This mindset changed when I took his class. This Precalculus class (which I took at the same time as my school's Algebra 2 class) scratched an itch that I didn't know I had in my brain. Not only were we learning things as well as why and how they work (which was a first for me), but my teacher also knew where the concepts we were learning got applied. Whenever I'd ask him where the subject we were learning was used, he would say something like "Oh, this stuff is used to calculate the shape of Formula 1 cars". In just that one year, I went from being indifferent to math to actually liking it quite a bit. Fast forward to now and I am completely in love with math. Although calc can be hard, there's just something about that is so... satisfying. And my teacher has kept his trend of giving examples of where things are applied whenever asked.
This comment is to you, Mr. Kramer. Thank you so very much for igniting a passion that I didn't know I had
it must be so satisfying for a teacher to hear “WOOOOAAAAAAHHH” all at once from the class!😂
Ikr
Big AGREE with you
ikr
As an educator for the past 20 years, yes, there is a sort of satisfaction with getting this sort of reaction from a class. It demonstrates engagement; But what's infinitely more satisfying is (assuming you have their complete attention and all in the same page) when you get them to truly contemplate a completely new or groundbreaking idea; something that challenges their existing notions and understanding. Even better, If you get them to start asking additional questions to process that idea, and they start asking those questions not just to you as the teacher or facilitator, but to each other in class, and then it ricochets back and forth between you and the rest of the class, those are truly the moments that make teaching satisfying, IMHO.
@@jcnbw01 could you please tell us about a time this happened if you can recall (edit: just out of curiosity, i've never been in a class like this and I kinda want to know more)
its kinda crazy because as a math student, you never are taught WHY things are the way they are, teachers really just tell us to accept it because that is the way math works. Even i was kinda in awe seeing this because i was never taught this in math.
UPDATE: Im currently taking calculus 2 in college, and this topic came up during class since we were covering root/ratio test, which deals with factorials. Even my calc professor didn't know exactly why 0! is 1 and I explained to her from this video!
Guess I'm lucky. I always get the explanation or am asked why.
actually your teacher's explanation is kinda same with this guy. you still dont have a sensible reason why 2⁰=1. you know its 1 cuz it has to be 1 for the rules on the other numbers. But you cant prove why 2⁰=1 is. Its exactly because thats the way math works. we better accept it as 1. you to better understand, let me give an example. 0⁰ is sometimes undefined sometimes it equals 1. we define it as 1 cuz it makes the things easier. we sometimes accept it as undefine cuz if we define it we make mistakes. In algebra its accepted as 1 and in analysis accepted as undefined. so its about us. not exactly cuz of the rule pattern.
Then your professor is shit because mine gave proof whenever there was one. And he also said when something was axiomatic.
@@FDE-fw1hd you're probably gifted
Ya education isn't imagination anymore its memorization now. Its not our fault though our system did this. See our ancestors did all the imagination and now we have just to memorize their works. Life is easy but boring at the same time.
2:50 -> The sound of having the most fantastic experience in a learning situation by having a teacher, who truly understands how to explain in a way that it sticks. Aha-moments are the ones that stick to your brain. I seriously just watched this video again, just to hear this again.
Me too
Hi.
My minecraft villager farm when i come close to them
Indeed, when it clicks, you won't forget it
I love in math when were doing something and im/the class like clueless the whole time until that aha moment happens
If every math teacher is exactly like this, the whole world of maths would be beautiful
he didn't know that there is 6.5 million students in his class
That's the beauty of it!
Now It’s 6.9M!!!!!!!!
@@nabranestwistypuzzler7019 69
Nabranes TwistyPuzzler lmao
High Guardian ikr
Lol I love how engineers and mathematicians see the world so differently. Mathmeticians appreciate the intricacies of numbers for what they are and all of their complexity. Engineers appreciate numbers for what they can do for them despite their complexity.
Mathematics, as a discipline, is one of the various conceptual worlds. It resides in the minds of people. Language enables sharing and discussing mathematics, so it becomes ever refined. But the primary source of mathematical ideas is the physical universe, for its natural laws are constrained by mathematics, not the discipline but the underlying pattern or subset of the whole of idealized relationships, known or unknown.
An example of a primary source of mathematics: Natural numbers relate to collections of individual objects, they are the collections' cardinals. An example of a non-physical application of mathematics: five mathematical theorems, three dreams, eight contradictions, four myths.
Engineers constantly deal with the physical world, it's their job. For them, the relationships between mathematics and its primary source, the real world, is fundamental.
Mathematicians constantly deal with the discipline of mathematics, of course. They try to squeeze the most of what they best know, and so, mathematics expands.
Philosophers also appreciate mathematics. Bertrand Russell's paradox of "the sets that do not contain themselves...." is an example.
Artists and mathematics? Of course! Tilings are an example. Fractals, another.
So, who do not love mathematics? Those who heard that mathematics was something hard, ugly and unworthy of trying. Those who prefer sports to thinking. And so on....
My daughter is 35. I have been teaching her mathematics for a whole year, for she asked me to. She was not too comfortable with what she had been taught at school two decades earlier. She takes free time for mathematics whenever she can, even though she has to work hard most of the day for a living. I am very proud of her.
Engineer and mathematician aren’t some mutually exclusive grouping. Im both an engineer and a mathematician
@@wafikiri_ wow
@@wafikiri_ There is yet another subset of people who hate mathematics, although unintentionally; those who were never taught about the underlying pattern because their teachers were unwilling or unable to explain the context of the lesson and simply told them to copy the formulas.
I wish I had a teacher like this who could explain how mathematics can be a creative pursuit rather than just rote memorization.
Man, I don't think about it that hard. I just get my daily dose of dopamine from doing well in math.
Admitting *_He's tons better than my maths teacher!_*
My maths teachers have all been awful in the past 3 years. As a result, everyone in my class hates maths.
Right?! Here I am with a guy who flips through curriculum-made PowerPoints for an hour and a half, wishing I could have a good teacher like this guy
Rip same
You don't actually need a good math teacher to do well in math.
In college you get to choose which professors class you sign up for.
If you're smart you figure out which ones are bad and avoid them. Once you're taking 300 level classes TRY TO FIND ONE THAT USES ENGLISH AS A FIRST LANGUAGE.
try.
Anyone from 2024?
just u
Idk why but I watched this again
🙋🏻♀️
here 😆
Ok
Me:why is 0!=1?
My math teacher:this is your home work today
Edit :தமிழ் (TAMIL)
Ahahahaha same then she will ask us why during the deadline
The fact that this is relatable is sad
Ironic because != means not equal
I have my buddy convinced that
4! = FOUR (REALLY LOUD)
Sameee
If I had had a math teacher like you when I was in school my life would have probably taken a different path. Keep doing what you are doing sir.
Kuba Marcin excellent answear, it's very relatable with my school variation of teachers
Kuba Marcin actually not he’s young teacher, but his chacteristic is tolerant ( in doubt), my teacher is more double aged than him and he still cool like him, but in some aspect you need some someone have calmness and expiriences, i’m not wanna judge him that his self - easteem quite high by first look, but I used to meet a similar guy like him, hence his positive out side while inside he feel very conflicted with students as same level as him ( sr for my bad english explanation )
Kuba Marcin, him being young is not the reason he's a good teacher. It's completely unique to every teacher out there.
If u dont pay attencion thats ur fault
@@cam_sus Apparently you didn't pay attention to his comment because that is not what he said at all.
Me as a programmer reading this as "why is 0 not equal to 1"
I WAS THINKING THE EXACT SAME THING LOL
Lmao
maybe it does
Lol same
Nice one! :-D
this is how college professors expect their students to react and engage but don't exhibit the same passion and energy as eddie
He knows hes succeeded when everyone shouts ohhhh.
Nithin Danday that must be a golden moment when you are a teacher
I'm also with this group.
they trolling him
I disagree entirely. 1! is 1, and you're saying 0! is also 1. Basically 1!=0! So you can cancel the ! from both sides and you're saying 1=0. 1 does not equal 0.
@@jazzabighits4473 No, you can't just cancel ! from both sides. Factorial is a complex function and ! is just shorthand for it, it doesn't work that way.
I went through all of high school without ever being taught what a “factorial” was.
I’m not joking.
Hahaha...I get the joke anyway.
Ahahaha.
Funny. Got more?
Well maybe you wore a headphones or somethin?
How did you graduate m8
kevin akbar No, it wasn’t in the curriculum. I graduated perfectly fine.
@@sin21ful Same, It seems easy though.
MR YUP all math up to and including some university level math is easy if you learn it in the right order
If all teachers, or even 1/2 of all teachers, were this good the world would be a much better place. This man can change the trajectory or lives.
As a US math teacher who has given that career up: if all students, or even 1/2 of all students, were this engaged and respectful (hell, if their fucking parents were even) then maybe you'd have teachers like this in the states. Poverty culture enforces poverty is what I'll leave you with.
It is GALAXY UGC 2885 in urr Pfp... Right???
@@academicpandemichighly dependents on the teacher. It’s a night and day difference on how the class interacts depending on what teacher we’re having
Awww we½2😊1
most of them are probably this good, its the kids who are shits
I watched this during high school and now I'm studying engineering. Thank you so much Eddie!!!!
Wish I had a professor like this, that actually had a burning passion for the subject, would have really helped!
My high school math teacher was a drunk fuck who got hired politically. He used to send me to buy him cigarets 5min before class ended...
@@stefan8991 lmao
@@stefan8991 what?? how did he not get fired for that?
@@stefan8991 wait how and like how are you allowed to be out of the school premises
@@asterisco3717 Uh?
I love his lesson at the end about Fourier! Those kids are lucky to have such a passionate math teacher. You can just feel his enthusiasm and passion for it when he was giving that explanation.
I asked my maths teacher how is a^0=1.
He said me in the following way.
a^0= a^(1-1)=(a^1)*(a^-1)=(a^1)/(a^1)
=a/a=1.
Note: "a" is any non-zero number.
I have no idea what you mean by 'a'. Could you please clearify it for me?
That's correct too...the diff is that ur one was theoritcal....woo's one was just observatory
@@shadowphantom6767 a is just a random variable choosen.. you can keep any variable or number in place of 'a'. Because anything power 0 is 1.
@@allin1club413 Ah, thank you! I've assumed that 'a' would be a variable, but I didn't get that a1 is supposed to mean a^1. I thought you meant a*1, since you don't have to write the multiplication sign (although the number should have been first if that was the case), but then the lower part wouldn't make any sense, so I assumed that 'a' would be something else.
To summarize: I understand it now, thank you!
My teacher taught me in the samw way too!!
@2:00 I was thinking the following way instead: 2^2 = 4. 2^-2 = 1/4.
Then, say, we multiply those two.
(2^2) * (2^-2) = 4 * 1/4 = 1.
Now, we know (2^2) * (2^-2) can also be written as 2^(2-2).
That would then make 2^0 = 1.
If i had you as my maths teacher my doggy wouldn’t have eaten my homework that often.
Lol
I used to say the same thing, and I ended up becoming a math teacher. I'm very similar to him by showing why things are, energetic, and breaking things down to simple levels. In my classes I have students that have gotten D's and F's in math for the last few years saying they've never understood math so much and about half the class say math has never come so easy. Despite that, there are also many kids that prefer to just zone out, not take notes, not attempt any work, prefer to try get on their phones, or try to just do anything other than math. All these kids say it's super hard... Anyway, my point is no matter how great the math teacher is, there are always students that will ignore instruction.
Because he would have eaten the dog
Sebbelito 69 hah
@@john-paulmathieu7195 how self reflected you are!
One more way of understanding this is- n ! is basically the arrangement of n different object in n spaces. Now, logically an empty set can be ordered in 1 way only, hence 0!=1.
i dont get it
It's to do with probability and the number of outcomes something has. e.g. you arrange 10 differently coloured umbrellas on 10 hooks and you must use every single umbrella you have (idk why I chose umbrellas but just run with me on this one), there are 10! different possible arrangements that you could have - since an umbrella cannot be chosen again once it is placed. The same is true for 0 umbrellas where there is 0! possible combinations which equals 1 (empty hooks can count as a possibility here since it technically fits the criteria of all umbrellas being "used").
There are 6 ways to arrange 3 objects. 3! = 6
There is only 1 way to arrange 0 objects. You can only arrange *nothing* in one way. So 0! = 1
this actually makes more sense, thanks
I was searching comment like this. Thank you
He is really a very great, interactive & a very patient teacher. Every word he speaks is to the point. I have seen a very few teachers who have really contributed their life in this teaching field & enjoys their profession.
For the a^0 i always had it explained to me as
1 * a^ any power = a^ that power
So like we had the list of powers, like 2^5 2^4 2^3 2^2 2^1 2^0 and then we added a *1 at the end of all of them. So we take 2^0 as 2 being multiplied by itself 0 times, so it is just not there, so the only result left is 1
That's perfect. I would say this is a better definition of powers. Instead of saying a^b is a multiplied by itself b times (when there are only b-1 multiplications. Like 2^3 = 2*2*2. Here there are only 2 multiplication symbols and hence 2 multiplications going on. 1st multiplication: 2*2=4, 2nd multiplication: 4*2=8).
.
A better definition would be a^b is 1 multiplied with "a", b number of times.
So 2^3 = 1*2*2*2
2^2 = 1*2*2
2^1 = 1*2
2^0 = 1 (we muliply it with 2, 0 times. That means we don't multiply it with 2 at all. So it's still 1)
Me: "alright I'm sleeping early tonight"
Also me at 2am: watching this because TH-cam Recommendations
it is exactly 2am when im watching this,,,,,,,ignoring sat practice
Literally me right now lol
At 1:18 am
Lmao literally me rn
3:16 am
Let's be honest, no one searched for this
But we're all happy it's in our recommended
So true
I searched
I searched cause i had factorials explained as the amount of ways you can arrange something and i was wondering how can you even arrange 0 of something in 1 way? Wouldn’t it be that theres 0 ways to arrange 0 things?
I looked up 0! On accident
Well I did
3:09
Teacher: this is what makes maths * pause *
Student : beautiful
Teacher * continues * interesting to me
Correct explaination for 0!=1 is
As we know n!=n(n-1)!
If we put n=1 here
1!=1(1-1)!
This will be equal to
1!=1*0!
so 0!=1
I hope this method is clear to everyone😃
we can consider a case where we have to select 0 objects out of n objects (unidentical) practically the answer will be 1 but formulated answer will be nC0 which will be
n!/0!(n-0)! = No. of ways of selection of 0 object from n objects
practically RHS = 1
therefore, n!/0!*n! = 1
given that 1/ 0! = 1
therefore 0! = 1
Arjuna batch se ho ka
@@Rajneesh938 nahi bhai sri chaitanya se hoo ( i mean tha )
He's really making every single student enjoy. Need a teacher like him
You're absolutely right,
I'm single and a student too,
I literally enjoyed it.
Yeah he’s awesome he’s Asian if you forgot
@@mattjendra2924 Why would you write this
@@morning5tarr 😤😤😤
@@kaajal116 why are crying ?
Did I do something wrong ?
This is the difference a great teacher can make - making teaching, and in turn learning, an engaging and fun experience for all parts involved!
1:22 I just realized he made a 2048 reference, also 2048 was released almost exactly a month before this video.
Oh so that's what it was. I get it now lol
his moves look like a "K" keta alien feels like.
Omg wow that’s so funny, I’ve been playing 2048 soo much recently 😂
That explains why he said everyone was familiar with that sequence
@@coyraig8332 no, these numbers are familiar because they're used for RAM and Storage specs.
I dropped out of Engineering in my last year and chose Real Estate as a profession, because I sucked at Maths, especially Fourier stuffs and Intergrations. I would never understand them.
But now after 10 years, as im reaching 30s.....Im watching many Maths and Physics videos on TH-cam and Im understanding everything.
I just wish I had teachers like him!
You can see the passion in this man's voice, the way he conducts himself, and the way he explains and projects his thoughts like this man really loves doing what he does, rather than spitting knowledge and expecting students to regurgitate without the students thinking, he makes the students think as he shows the magic and how fascinating math is theoretically. I always loved teachers like that where they truly enjoy doing what they do. They are what makes learning in school so fun and those are the teachers I hold the upmost highest respect for.
When I did it in this way, many pupils were more than sceptical and just wanted to memorize blindly. And because the majority is silent, the loud losers and their very "protective" parents dictate the school what to do and how to do it.
YES! And the way he explain that just messing around with numbers and logic can be so fucking important for future needs beyond our understanding makes ME want to learn math! And i fucking hated this shit through high school. This teacher is basically saying: Learn stuff to just mess around with it, you may just discorver something
I'M SMART BECAUSE I USE TH-cam. I'M GOING TO RAISE MY KIDS TO NEVER GO TO SCHOOL. EVERYTHING CAN BE LEARNED ON TH-cam.
@@CooManTunes but you should find a way to clear his/her doubts
I have utmost respect for John Gabriel the author of New Calculus channel on youtube, he has discovered and shared the most remarkable things in mathematics which I had the chance to encounter so far
'The point is that it doesn't matter if it can be used for something, it's that it has a consistent set of rules that is meaningful'
see how every other teacher replies 'you have to learn it because it's on the spec' or 'you just have to know it', this is a much better way of saying pretty much the same thing.
Weird how I read your comment the exact time he said that.
My past math teacher is great at her field, but she's too fast and she tends to story tell my seatmates don't know what we're talking about anymore.
if you do programming it is useful... e.g. implementing a fold operation with multiplication operator.
If you know 0! = 1, you will use the correct identity value :)
As a programmer, the 'pure' maths is more useful than 'applied' maths, the names are misleading.
pure math is like a philosophy. it may not be applicable often but it is meaningful.
666 likes
William Yep! And if you do probability, for example, if you start studying for the actuarial exams, you will need to use 0! in the formula for combinations: n choose r formula - as n choose 0; as well as permutations: n P r, as in n P 0. That is the only way that combinatorics and their use for probability makes sense.
Trying to imagine how my life might be different if I had just ONE math teacher who taught with this energy and cared this much about me understanding math.
true
I feel ya
I am learning math the hard way at university after years of total lack of knowledge. I have been on the edge of crying so many times. The fact that I can understand this lecture is already a victory to me.
You realize it's not just maths. It's pretty much anything. It really boils down to nurture. If you have a really good mentor who knows his shit and also knows how to convey that to you. Bonus! That's where luck plays in.
Everyone has potential but it requires the right person to bring that out of you. Sure you can say why not do it by yourself? Trust me you can't. Some things you have to do it with others. It's also the reason why we humans are social beings. I don't want to bring psychology and philosophy. Coz I can go all day.
The greatest maths teacher is actually... you because only *you* can push yourself to learn it.
Here is an another reason why a^0 = 1.
According to the law of exponents:
(a^m)/(a^n) = a^(m-n)
Let's take any number raised to any power. Let us take a^x. Now let a^x = y
Then, y/y = 1
a^x/a^x = 1
According to law of exponents
a^(x-x) =1
a^0 = 1
I think one of his most overlooked skills is letting his class talk to each other. At first I was annoyed by their noise but if you pay attention to them they get excited when new info is being presented, they are sharing their epiphanies and genuine interest
He also stops to look around with a smile, he is often seeing how he can interact with them if he overhears a student staying on topic and talking about the subject
i think he stops bc students use the cover of the noise made by the teacher to have their own conversations. When he is silent its easy to spot whos being loud
source: im a student who does this sometimes
Not always, when there is interest it's ok, but it's horrible when it's just an irresponsible group.
The teacher should always have the authority to shut them up.
But obviously this video is a totally different situation.
Was wholesome hearing their reactions
This is excellent teaching. Here I was expecting him to pull out some obscure logical lemma some mathematician made three centuries ago to account for some edge case for where 0! not equalling 0 creates some kind of contradiction, but it’s just... the pattern continues. A number divided by itself is always 1. Damn. I can’t believe I hadn’t given this thought before.
EDIT: YES I GET IT ZERO IS A SPECIAL CASE STILL. The pattern only continues because the rest of the factorials exist in the domain of the positive natural numbers. I swear some of you would freak out at "a prime number is a number that can only be divided by itself and one" if I didn't also say "except for 1". It's almost as if special cases have reasons for existing that aren't entirely self-consistent, but are important for mathematical patterns to continue in a logical fashion.
Zero divided by itself is undefined, not one.
@@OtherDAS Not necessarily. In another video he explains dividing by zero. And He explains that division is just repeated subtraction (just as multiplication is just repeated addition) until you reach 0.
If you subtract zero from zero you are already at zero. Of course you can argue that you can subtract it zero times, because you're already at zero before you subtract even once. But if you don't subtract at all, because you are already at zero, you're not dividing (repeated subtracting) at all and therefore by definition not dividing anything.
Basically, 0/0 can be either 0, 1, or undefined, depending on how you look at it
@@kindanooby2988 It can also be anything else. A group of zeros always make a zero.
@@OtherDAS yeah exact 0/exact 0= undefined
0^+/0^+= 1 ,,,,, and 0^-/0^-=1
What a great teacher. Schools need more people like him with the enthusiasm he shows and the ease of explanation to get things across he has.
He didn’t even give the complete reasoning for a^0 😂
It’s because (for example) a^2 / a^2 is clearly 1 because it’s a number divided by itself, but you could also simplify it by subtracting the exponents because they have the same base (a), so a^2 / a^2 can also be written as a^0, which is 1
It’s more than just continuing a pattern because we have no reason to believe we shouldn’t, there’s an actual mathematical explanation
Rare footage of a teacher _actually_ teaching.
It's not that rare lol
Shudhanshu Shekhar Mishra The fact that us three are even capable of typing these sentences in decent grammar is proof that teachers teach.
men
Dearth of Doohickey’s I
Kelly Appel is the time of my life for the new year
When I was a child,seeing the ! On the calculator,i thought WTF exclamation mark doing here
Haha same
XD
same
When I was a child
Entered 10/3 = 3.3333333333333333
Mom! I broke the calculator!
The “ohhhhhh”s when he explained it was golden
You could hear in the voices that the students were MAD at the solution
The way he commands the respect of his class to all shut up and let him finish is amazing.
It goes to show that a good teacher who is passionate about his material is unbeatable when they start explaining *why* they are so passionate.
Ahhh Wire
So, a practical explanation:
Factorial is an operation that says in how many different ways you can sort a determinate amount of options.
So let's just change "options" for "cubes".
In how many ways can i sort my 6 cubes? 6! or 720
In how many ways can i sort my 5 cubes? 5! or 120
In how many ways can i sort my 4 cubes? 4! or 24
In how many ways can i sort my 3 cubes? 3! or 6
In how many ways can i sort my 2 cubes? 2! or 2
In how many ways can i sort my 1 cubes? 1! or 1
In how many ways can i sort my 0 cubes? There is only one way of "having no cubes", so 0! must be 1
Gabriel Silva Rocha oh wow, thanks so much haha, i didnt watch the video yet and just browsing the comments :)
Thanks, I like this reason better than the video's
@@derek9511 Yeah, theoretical explanations tend to be better, and practical ones tend to be more likeable
Wow that was simple.
This is a more correct way to explain 0! than the video explanation. I mean, that's fine, but this is better because it doesn't use the definition of n! as "the product of every positive integer equal or smaller than n" and then finds a way around it. Another cool way to explain 0! is by introducing Euler's Gamma function, which also gives you values for any real number's factorial except for negative integers.
That was the longest time I focused on math since I was born.
Never would I have ever thought, that I myself, would click on a video to willingly learn about math on my own because I was curious.
Instead of being forced, if our curiosity is engaged, why'd anyone not learn things? This allows us to study what we desire and choose to.
And we can learn other subjects without having to give exams for them while focusing on the subjects that we want to excel in.
lmao same. Pretty interesting though
this guy's passion for the subject is infectious. Seems like a great teacher.
The worst thing about the video is that, "It ends!!!"
Suddenly, out of nowhere
It ended when I was reading your comment lol