Main site: www.misterwootube.com Second channel (for teachers): / misterwootube2 Connect with me on Twitter ( / misterwootube ) or Facebook ( misterwootube)
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."
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.
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 ✨😊
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
My favorite argument for why 0! = 1 is the Combinatorical argument for it. In Combinatorics, n! is the same as the number of unique ways you can rearrange n items into n unique slots, because you would have n choices for where to place the 1st item, n-1 choices to place the next item, and so forth, you multiply all of your choices to get n!. So 0! should therefore be the number of ways to rearrange 0 objects in 0 slots, which would be 1 because there's only 1 way to do it and you cannot change it.
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.
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.
@@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.
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 graduated in Electrical Engineering from one of the top universities in the world 35 years ago and no one has ever shown or explained to me these proofs and I accepted these as truths or axioms. Mad respect to this teacher!
apparently one of the top universities in the world doesn't teach its engineers the definition of factorial nor how to distinguish a proof from a fun fact..
@@francescom2027 @francescom2027 i think you should learn to read the comment before making such a stupid reply. He was implying that they didn't teach him _why_ 0! = 1, not that they didn't teach him factorial in general. There is clear difference between the _how_ and the _why_ Knowledge of how concepts in mathematics work provides a better understanding of the subject in general, explaining why 0! = 1 is not a "fun fact", as you would appear to think Honey, you might want to review your levels in reading comprehension and mathematics rather than nagging at random people all day.
@@youssefbencheikh8637 the explanation in the video is not a proof but a fun fact. 0!=1 by definition of factorial. This definition is necessary because every factorial ends with 1!, and: 1!=1(1-1)!=1*0!=0! You'll convey that you don't really need Princeton for this...
actually it isnt a proof and correct. We defined it because ıt works us. when we need it we accept it like that. Think what is union sets of empty ? can you connect empty things ?
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 RU-vid 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
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
@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.
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!
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
I do appreciate the exponent view going backwards, which was one of the ways I introduced extended exponents in my class. Doing that for factorials was something I haven't seen explicitly spelled out before. Also great was the teachers clear love for the meaning and consistency properties of math - the "it just works". This was a very nice presentation. I do wish the more general point was also presented - that empty products are always 1, just like empty sums are always 0 - and the why for that given, but obviously I have no idea what else he presented to his students after this 6 minute fragment. I just like to show kids how you can break products like Pi(0
Simply awesome , Eddie. Most of the problems are solved not with hard math, but with an out-of-the box approach ... simply coming backwards, as you showed. Cool !
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 really respect teachers that love and breath their work, and actually motivate and create enthusiasm in students. Makes learning look funny and more accessible
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 RU-vid and Im understanding everything. I just wish I had teachers like him!
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 😂
this is what I missed in school, I should've studied harder back then. I can see the enthusiasm explaining the logic of how certain ideas gets formulated. thanks for the video
that was a fun riddle, well presented, it is all about patterns. working with programming consistency and patterns are things you will encounter all the time, but also in other forms than maths
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?
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
Congratulations, Mr. Woo. You've earned a subscriber out of me. I have no idea why RU-vid suggested this video to me--I love Math--but I am glad it did.
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.
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..
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
I saw your video a few years prior and then my instructor asked this question in class and it was something no one had ever studied before but thanks to this video I knew 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) .
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.
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)
i figured out the powers thing by myself a few weeks ago and was a little skeptical that it was the actual reason, so seeing someone else teach is a huge relief. didnt think to apply it to factorials tho
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
I'm commenting here so that when anyone after years like my this comment, then I will get remember these days which will not come back in my life again. 😊😊
@@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.
That square wave you drew. Those sharp edges lead to a lot of harmonics. Practically, this means that a three phase system needs a larger neutral line than a three phase system that is just a sine wave (ie no harmonics).
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.
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.
I don't know why but whatever I am currently studying (not on the phone) at tuition, the videos related to those topics are being recommended to me by the RU-vid out of nowhere. And 0! thing was revolving in my head since many days and again I got a recommended video related to it. I think RU-vid has become a mind reader. 😂😂😂
Woa I just realized that I'm actually watching this video on the same date just 10 years later ?! That's crazy but honestly really nice pls never stop uploading
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 someone who has an engineering masters, I've always known what the values of these were and accepted it as fact without ever thinking about it. I've done the highest level of maths through secondary school and engineering maths through university. This is the first time I've seen this explained and I've had some amazing teachers in that time. Good job!
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 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 got my answer finally after about maybe 8 years... I was expecting something more complicated but it was kinda simple! Also I think I finally understood the application of using Fourier series. Thank you so much
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.
For exponents of like bases you simply subtract values when dividing. so a^10/a^3 = a^7, but a^10/a^10 = 1 for obvious reasons. Therefore, a^(10-10) = a^0 must also equal 1.
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.
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.
Love this channel and all he provides. Why does this pattern not continue though into the negatives (-1!, -2!, etc) though like the proof on the right? Seems arbitrary that it didn’t break down going to 0, but does break down after that.
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 see a lot of comments talking about how other teachers should be like Woo. I think he’s an amazing teacher. But I also think a lot of people disregarded their teachers in highschool, and now see teachers on the internet like Woo and see how good they are, but are blinded by their teen angst and dislike of highschool, so don’t realize how good their teachers were.
