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."
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
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.
@@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.
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.
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 ✨😊
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.
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 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
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 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
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
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!
@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.
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 !
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..
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
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
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
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
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 😂
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!
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?
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
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
For those who are hungry for more maths, I am a college student and I don't blame HS teachers not showing the real reason why 0! = 1 because the real proof involves an indefinite integral called "gamma function", which you solve by integration by parts, and this function defines factorial for any number, even 0, even negative numbers and fractions, when you try to calculate the factorial of 0 by gamma function, the result is one, I really recommend reading about the gamma function and stuff because it is really interesting, and just a little teaser, the factorial of 1/2 is the square root of pi divided by 2 :)
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 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)
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.
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.
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.
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 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
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 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.
Congratulations, Mr. Woo. You've earned a subscriber out of me. I have no idea why TH-cam suggested this video to me--I love Math--but I am glad it did.
5:50 Fun fact: Complex numbers were found because mathematicians where competing to solve a then unsolvable problem. They wanted to figure it out then keep the answer secret so that only they could solve these problems lol, literally a "Anything you can do I can do better" thing. Veritasium has a cool video on it called "How imaginary numbers were invented", and the thumbnail reads "epic math duel" lol
@@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.
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.
Another way to answer is would be to think: how many unique ways can you arrange a sandwich? You're going to a really specific kind of deli shop, where the bread is always the same, but you have a choice between 2 cheeses, and then 3 meats, and then 4 condiments, and so on. In the case of 3!, this means you get [1 bread choice]x[cheese choices (2)]x[meat choices (3)] possible unique sandwich options. This also works well to explain visually with a flowchart. One branch into two branches into three and so on. You just count the number of branches at the end. This is why when you go backwards from 3! to 2!, the answer is 2 because you can only make two unique arrangements. And when you only have bread, there's only one thing there. Why is 0! = 1? Well, how many ways can you arrange nothing? Just once.
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.
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
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.
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.
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.
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 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 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*
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
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👻👻😎😎
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❤❤❤❤
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**
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
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.
Shouldn't that be 0?
@@ankusaini6092There’s 1 way to arrange nothing
Oh yeah, anagrams! The only practical use I know for factorials
Amazing!
@@aj76257 which is?
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.
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
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
Anyone from 2024?
just u
Idk why but I watched this again
🙋🏻♀️
here 😆
Ok
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.
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" :)
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
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!
May I ask what was th university you attended?
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 ?
Who are watching in 2024?
Ya'm
Me
Me❤
I can't ignore these videos at 2am
@@malakilikemokaaa1385 where are you from?
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.
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
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 love how engaged the class is! It really makes learning so much better.
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
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.
I've read Fourier's original book on heat transfer, and he was absolutely motivated to develop the OG fourier series to further study heat transfer.
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!
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
Fun Fact: You didn't search for this.
Lmao i did
I did
Fun fact : You have copied this comment from someone else.
@@vishnuvr4706 ;)
Recommended by YT, Idk why.
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
The first full science-related video I watched after graduating form an engineering degree 3 years ago. Thanks
*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 👩🔧
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
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 !
You're an Australian Icon. These lessons are fantastic.
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.
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
Remember seeing this in my engineering statistics course. This was a great refresher
I've never ever found maths entertaining. This guy is amazing. 18M views. Well deserved. Holy shit. Dude just opened up my eyes. 10!/10!
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😂
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?
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
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
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
"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 👍👍👌
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
Your explanation has solved my doubts for years, thanks!
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
“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 😂
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!
The students are probably the age of teacher now .
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?
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.
I watched this during high school and now I'm studying engineering. Thank you so much Eddie!!!!
This was the most entertaining math lesson I ever listened to in my entire life.
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
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
For those who are hungry for more maths, I am a college student and I don't blame HS teachers not showing the real reason why 0! = 1 because the real proof involves an indefinite integral called "gamma function", which you solve by integration by parts, and this function defines factorial for any number, even 0, even negative numbers and fractions, when you try to calculate the factorial of 0 by gamma function, the result is one, I really recommend reading about the gamma function and stuff because it is really interesting, and just a little teaser, the factorial of 1/2 is the square root of pi divided by 2 :)
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!
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.
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)
We definitely need more teachers like these to ensure that humanity remains curious! 😇
Ive never heard so much laughter in a math class
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
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
Nice Explaination, you deserve better students.
This guy is a very gifted teacher, I wish we could all be so lucky to get an instructor like this.
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...
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.
9 years ago ,I wouldn’t have appreciated this as much as i do now👍
I can't believe I'm watching this at 4am in bed wanting to sleep, and I really enjoyed it!.
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
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
I am clearly unfortunate enough to not have met or got a mathematics teacher like him. Those students are indeed very lucky!
i love math teachers that love to teach. it makes info so much easier to absorb
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
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.
this guy's passion for the subject is infectious. Seems like a great teacher.
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
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.
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.
Congratulations, Mr. Woo. You've earned a subscriber out of me. I have no idea why TH-cam suggested this video to me--I love Math--but I am glad it did.
5:50 Fun fact: Complex numbers were found because mathematicians where competing to solve a then unsolvable problem. They wanted to figure it out then keep the answer secret so that only they could solve these problems lol, literally a "Anything you can do I can do better" thing. Veritasium has a cool video on it called "How imaginary numbers were invented", and the thumbnail reads "epic math duel" lol
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
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
When everyone just said "Accept it-" 😂
Another way to answer is would be to think: how many unique ways can you arrange a sandwich? You're going to a really specific kind of deli shop, where the bread is always the same, but you have a choice between 2 cheeses, and then 3 meats, and then 4 condiments, and so on. In the case of 3!, this means you get [1 bread choice]x[cheese choices (2)]x[meat choices (3)] possible unique sandwich options. This also works well to explain visually with a flowchart. One branch into two branches into three and so on. You just count the number of branches at the end.
This is why when you go backwards from 3! to 2!, the answer is 2 because you can only make two unique arrangements. And when you only have bread, there's only one thing there. Why is 0! = 1? Well, how many ways can you arrange nothing? Just once.
I think all people want a teacher like him
I know I did growing up
And some want to be a teacher like him😋
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!
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
Nice one TH-cam. Thanks for recommending this NOW and not these 9 years ago when I was in school. Very cool...
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.
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
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.
Eddie Woo, you are an amazing teacher (and I taught for nearly 30 years!). I wish you would have been my math teacher!
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.
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
Wish I had teachers like you in my College days ❤. Respect 🤘🏻🤘🏻🙏🏻
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
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
Love how teachers can be humourous
"I know math can be used to stuff thats nice"😂😂😂