Why is 0! = 1?

I can't believe I'm watching this video for entertainment

Teacher: "and i divided by one" Class: "WOOAHHHH!"

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 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.

Why isn’t every math teacher like him;(

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.

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.

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”.

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!

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 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

How many people have asked their teachers and were told “...because it just is”

Bank balance = $00.00 This guy: Nah fam you got 100 cents💀

I love how engaged the class is! It really makes learning so much better.

Meanwhile my math teacher is: "That's just the way it is. Don't question it!"

Wow math is actually interesting when someone knows how to explain it well

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 :)

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!