What is the basic building block of all mathematics? (A surprising answer!)

[@Mtech800]

you know he's a good teacher when he's got me watching these videos for fun

[@sahildinkar4325]

Same here...it's so much fun

[@missbyu9383]

Yes, he is interesting and motivate students to learn.

[@skylar011]

Literally was going to say.. "Sometimes I watch these videos for entertainment." You got me bro lol.

[@pyrite2060]

same

[@luckyl8749]

Same

[@dddhhh2612]

I think Eddie Woo might just be the basic building block of education! This is what a great educator look like!

[@XiaoMof]

@JimmyMontoya He definitely excels as a teacher, because he understands how a person learns. If a teacher does not understand how someone learns they are no teacher at all.

[@milanstevic8424]

@@XiaoMof but how do you call people who were taught by mostly non-teachers? because we need a name for this type of humanity we're stuck with. if we don't come up with it, historians from the future surely will, if they ever come to be.

[@keithrouch4373]

I think “non teachers” are a fact of life that nobody can really escape.

[@vitalyavolyn]

"But what is three?" *vsauce music kicks in*

[@TheMistforman]

I wanted to say it was a concept.

[@davearbuthnut241]

@@TheMistforman You're thinking of infinity :)

[@LucisFerre1]

@@TheMistforman , you are quite right. "3" represents a concept.

[@fazalahmed2329]

3 is a "Name".

[@bluthemeth]

@@fazalahmed2329 “3” is an amount. “3” is a number “Three” is a word

[@roguevector1268]

"I don't want you to shout out any answers." Mr. Woo is flexing on us with how much engagement he's getting.

[@desirebrunoduval3901]

I am a retired instrumentation technician and a Maths lover....I must say this guy is a wonderful teacher. :)

[@gretawilliams8799]

Desire Bruno Duval Do you realize that reality is based on logic and reason. ??

[@qwertywypi1337]

@@gretawilliams8799 are u against him? just asking

[@hughessoso2003]

YEAH, I wish that I could have a teacher like him, when I was at school. XD

[@skilz8098]

@@gretawilliams8799 Not always! Reality is also perspective, intuition, and will power!

[@pebblepod30]

Desire Bruno Duvel - That sounds like a decent job how do you get into that? Electrical engineering? A certain trade?

[@LyfSukz]

I haven't even watched the whole video yet, but i love how at around 0:30 you kill that chatter in the background without even saying a word and without breaking your train of thought. It wasn't even a particularly angry or threatening look either, but it perfectly got the point across.

[@craftsmanwoodturner]

That's what happens when a teacher is so good, and has earned the respect of all of his pupils... He allows a certain level of chatter as his pupils take the ideas on board, but doesn't let it stop the forward progress of the lesson.

[@tengkuizdihar]

>division by zero >YEEESSS wow that is some enthusiastic student. Probs.

[@psychwolf7590]

Hahaha

[@gretawilliams8799]

Fuck off then

[@jamiemckay6079]

@@gretawilliams8799 bruh

[@thetooginator153]

I love it that an enthusiastic, young, Australian math teacher has almost a MILLION subscribers! I’m a subscriber and I haven’t taken a math course in many decades. He just makes it fun and interesting.

[@BeckBeckGo]

Hell I’m a student of pure mathematics and I watch this guy teach high school.

[@thetooginator153]

@@BeckBeckGo - I’m envious! That sounds pretty cool! One thing that rekindled my interest in math was the advent of home computers (yes, I’m old). It’s AMAZING how computers take the drudgery out of math. Can you imagine using a slide rule? Yuck!

[@thetooginator153]

@@BeckBeckGo - Oh, and if you decide to go into the private sector, be prepared for HUGE paychecks! Pure math has so many high-demand uses, you will be shocked at how much you will be making. Just a tip though: try to get some statistics and computer science in your repertoire (if you haven’t already).

[@dylangwyther4338]

There’s a mil of us now boooiiiii

[@vkak1]

Damn this guy is a fricking king. Makes a math class soooo much fun. I’d love to rewind time....jump on a plane to Australia just so I can have classes under him

[@JashXD]

yea his best videos are from 2014-2016

[@ryanstevenson7933]

For some reason I always imagined the door on the other side of the room

[@jordanweir7187]

You're a brilliant teacher dude, this entire generation can benefit from how you make the material inspiring and intriguing, keep doing what you're doing.

[@chateau1897]

That's like a dream class to be in ! The students are also joining in to spiral their ideas and ask the what ifs and it's interesting to listen to every questions.It gives much more information and curiosities to be answered. A real great dedicated teacher. My respect to you on being able to make the students become enthusiastic!

[@keithrouch4373]

He actually understands math which I think a lot of the teachers I had didn’t. Math is my biggest source for frustration and failure. And I love these videos!

[@ranjittyagi9354]

Same here. 😠 I try to keep calm nowadays about this fact as anger can't repair the damage already done.

[@laman8914]

This guy is a Master Teacher. Every time I watch one of his math videos, I go "Woo". He always brings something you have taken for granted or just never thought about it, in a new perspective in a very simple way. I never thought of numbers in terms of sets, even though I have used both in math and elsewhere. Changes you entire perception of life. Thank you Mr Woo

[@biggles258]

Great progression through your topics. What I love is the way you safety-net each step. When I was at school/college, back in the day when white-hot technology was a quill, it was so easy to get to the stage in a lesson where the current concept on offer didn't quite find the mental hook that it was meant to hang on. The lecturer would already be onto the next part of the lesson and panic would set in. You have the wonderful knack of anticipating when those hooks haven't quite formed and providing that extra material.

[@AlexandreAbreu1]

As a professor, I can say that you are an inspiration to me. Congrats on being an amazing human being. Love from Brazil!

[@erygirl]

I wish we had more of these teachers, they help make learning fun and engaging. I would have loved to have him as my teacher👏👏👏👏👏

[@jamesmosher6912]

Such a great teacher! Love your videos. Don’t know him, but seems like such a great man. Someone who can approach these things with that passion. The world needs more Eddie Woo’s.

[@sobhinthomas5048]

What an awesome interacting class.I wish mine was like this

[@abhinandanmalhotra8519]

He's really Passionate for what he does ! And this makes me to watch his videos even if I have intuition for the topic, it feels more than intuition ! He's a great teacher !

[@elltwo8393]

The two primitive “building blocks” of math are sets, and the relation “is an element of”, that tells us if something is or is not “in” a set.

[@lorax121323]

The notion of a space and a vector isn't really reducible to sets. It can be defined in terms of sets, but you wouldn't be able to find anything in sets themselves that tell you that they can be graphically represented in any way at all.

[@fullfungo]

@@lorax121323 Well, there is nothing in the number 3 that tells you that it can be represented graphically either. That doesn’t stop us from drawing 3 dots, 3 cows or 3 vectors.

[@YJ4]

Good teacher!

[@user-mj7yd2oq6j]

YJ.

[@kanniicapture]

i like your class i havent had a teacher that was engaging and this fun to learn from since a while. thank you for your hard work and effort!

[@xlalmoses6894]

I have no idea how a good teacher you are, please keep going,

[@LightAlkmst]

Great teacher. Reminds me of the philosophy of statistics and probability course i took.

[@arks8089]

Incredible teacher, I wish I had a teacher like him👏🏽👏🏽👏🏽

[@yuurishibuya4797]

Your videos gives me nostalgia and early morning high!

[@MadaraUchihaSecondRikudo]

For the record: Atoms are indivisible in the sense that if you take a block of iron, and cut it in two, you have two blocks of iron. If you take two atoms of iron and cut in two, you have two separate atoms of iron. If you take an atom of iron and cut in two, it's no longer iron.

[@AzureKyle]

Exactly. It's no longer iron, it's an explosion.

[@MadaraUchihaSecondRikudo]

@@AzureKyle Not in the case of iron, too stable. You'd just get 2 silicon nuclei or something. But the point is it's no longer iron. An atom can be divided, but only by changing its nature.

[@AzureKyle]

@@MadaraUchihaSecondRikudo I was making a joke, because usually when you split an Atom, it causes a nuclear reaction.

[@MadaraUchihaSecondRikudo]

@@AzureKyle Yes, but not iron atoms :D, they don't cause a reaction since they're too stable.

[@IceMetalPunk]

Regarding the "if you have a headache thinking about infinity, that's probably a good thing" introduction: there's an infamous story that Gregor Cantor himself went mad dealing with infinities. While that's a bit reductive, there is some truth to it: Cantor was bipolar, and between the stress of his work and the stress of his colleagues dismissing his work, it aggravated his symptoms. So if you feel like dealing with infinities is too stressful and driving you mad, you're in great company! 😁

[@ianoliver3879]

A brilliant teacher. Thank you.

[@mthurston1978]

I wish I had this guy as my teacher - his teachings on RSA encryption are the best I've seen

[@Smownage]

The more technical answer to "what are negative numbers?" which was asked in class is: take the set of ordered pairs of non-negative numbers (so (1, 2) is different from (2, 1)). Then calculate the difference between them, in the above case, the difference is 1. An integer number is the set of all pairs of whole numbers with the same difference. So (5, 3) and (8, 6) are both in the set representing the integer "2". And you can check that addition and such works, regardless of which pair you choose: (5, 3) + (8, 6) = (13, 9) says that 2 + 2 is 4, even though we chose different pairs to represent the number 2. A negative number is just the same thing, but in the case where the second number is larger than the first number. So (5, 3) is part of 2, but (3, 5) is part of -2. And again, you can check. (3, 5) + (8, 6) = (11, 11) says that -2 + 2 = 0. Of course, this is not how anyone actually thinks about negative numbers: the point is that, in mathematics, we always want to avoid contradictions. Checking that this works tells us that, provided there are no contradictions in the positive numbers, a simple structure, then there are no contradictions in the negative numbers, which are more complicated.

[@arrrg3846]

Would love to watch a documentary similar to the Brit show "63 up" (but not wait so long) where some of Eddie Loo's students are interviewed to see where they are now and what they are doing. His teaching style is so *_engaging_*, I can imagine a number of students found him and his class inspirational.

[@paulreader1777]

If you have transferred some knowledge to one person in a group with whom you are communicating you have done a wonderful thing - listen to the response from one individual in the class at 15:45 or 15:46.

[@martinepstein9826]

It's awesome that you're able to devote class time to so many fascinating topics outside the core curriculum. I've talked to high school teachers who say they're really constrained by the need to cover a mandated list of topics and prepare students for standardized tests. I'd be interested to hear how you navigate this issue.

[@toanhien494]

I think it's extra classes, in which the students volunteer to do it.

[@jela1277]

earned a sub! its amazing how this was never explained in all my years of schooling

[@marcdavies7046]

I just love that the reaction you get out of your class for this complicated subject is "Yes!'... such a beautiful question.

[@cheofusi3562]

I hope I get to meet this guy one day...His brain's programmed to impart knowledge so effectively, systematically and logically to his students....using Logic!!!

[@ArtanisKizrath]

Wow! This video just gave me a profound philosophical amazement.

[@markrigg6623]

Maths is a subject where the quality of the teacher really, really makes a difference. I hate maths but his lectures are great to watch. A master class in creating engagement.

[@RR-po1ih]

Thank goodness he understands that teaching is SO much more than the subject matter. If there were only more people in every profession that cared and tried as hard as he does....the world would be a much better place for “life”.....I also believe he is a life long “learner”...and communicates that to his students through his enthusiasm, teaching, and humility....

[@Wombah-rc6zz]

There should be the "Woo" standard named in honor of Eddy & any teachers NOT achieving this standard of teaching excellence, should get retrained or told to try a different career path! Some of my teachers had all the energy & motivation of a stone! How can the likes of these motivate & inspire their students? Eddy makes maths not just interesting but real FUN!!!

[@jursamaj]

Given the way societies tend to treat teaches, it's amazing any of them can be enthusiastic for more than a couple years. :(

[@Lazorkite]

Pop smoke

[@livethefuture2492]

At least we have the internet to allow great teachers the recognition they deserve.

[@davidrobie6693]

My answer to the question was addition/subtraction. Multiplication and division is just addition/subtraction ... done over and over.

[@robert1900]

What a role model for young people.Learning is fun -you just need the right person to lead,guide,coach and encourage

[@samwise8333]

Number are just used to represent something. In binary system we use 1 and 0 to represent a particular no. We use diff permutation of combination of 0 and 1 to represent no.

[@erfho8y]

This guy is one seriously great teacher.

[@vic123]

It's amazing high school kids have the opportunity to have a teacher like him lol. When I was in high school, our teacher was half asleep dragging through trig. This man is teaching his students things I didn't see until a fair way into university. Great guy tbh

[@ShepherdV]

I just love your lessons, for the question you asked, I'd ahve answered logical thinking.

[@josephortiz9837]

An amazing teacher

[@TheZenytram]

15:45 the knowledge has reached his destination.

[@tabrezshamshashmi4043]

Sir, You will change my perception about world

[@argentum001]

My response would be: quantities. Numbers are just one way of expressing quantities, but they aren't the only way. Now going to watch further to find out the actual answer ☺

[@joshuasims9056]

Fantastic, thank you.

[@sreeramp.v7674]

Super interesting class sir you are not a human You are a machine full of ideas

[@fayetoliver562]

Awesome Mr. WOO! Finally, the WHAT & WHY!

[@maths.explained]

Amazing, thank you Eddie. Is this based on the ideas of Bourbaki?

[@victorlc.vabeiryusa7458]

Damn i love this so much

[@AfreenKhan-ll5zm]

Sir you are my role model 🙌🏻🙏 Love from India 🇮🇳

[@painpeace3619]

Beautiful and amazing 😊

[@midwestrailroadproductions8116]

I love your mushroom cloud drawing.

[@jimgardner6394]

I was waiting for him to hold up 3 markers and then take 4 away to demonstrate what -1 looks like! I wasnt entirely convinced the analogy with matter helped because there you are subdividing something down into smaller and smaller elements but with Mathematics there are a number of concepts such as symbols, rules (axioms), sets, groups etc that complement each other. Is the building block of language letters?, symbols? grammar?

[@larswinzer7556]

I can not express how mind blown I am after watching this video . I discovering Eddie Woo's channel from a suggested video after 3brown1blue video that talked about group theory. Coming into this video thinking the basic building blocks of math being ratio's and portions(negatives are reflections and imaginary are laterals) gave me the understanding that dividing by 0 would take away the starting point or cancel out measurement (I thought of 3browns1blues linear scale). I sat in my chair mind blown not knowing if I was peaking from the weed or actually having an epiphany. I thought dividing by 0 would create unmeasurable chaos. After watching his next video to find out why dividing by 0 is undefined I feel so inspired after this I feel i have direction and want to pursue a degree in math.

[@jamesc3505]

Late to the party, but my 2c: I think you can get a decent amount of math from 4 things: 0, incrementation (adding 1), repetition, and inverse (opposite operation). From 0, repeated incrementation produces addition and the natural numbers. The inverse of addition (or the repetition of the inverse of incrementation) produces subtraction and the negative numbers. Repeated addition produces multiplication. The inverse of multiplication produces division, and the rational numbers. Repeated multiplication produces exponents. The exponential function can be inverted in two different ways to produce the root and logarithm functions, complex numbers, and a more (but not all?) of the real numbers.

[@laurasalo6160]

Oh, this reminds me of why i love mathematics so much!

[@Woodman-Spare-that-tree]

When he talks about the English numbers 1,2,3, they are actually based on counting the number of angles in the written symbol, not on counting the number of straight lines in the written symbol. The number one (1), if you look carefully at it, has one angle inside it, and the number (2) has two angles in it, and so on, and so forth. Look at the number (8). If you write it without curves, it has eight right angles inside it. etc

[@rickshenchaze3609]

I'm a computer science student and no longer need to do maths but here I'm enjoying your videos i miss doing maths.

[@luizantonioponce1368]

Wonderfull!!

[@theevolutionaryalgorithm5947]

My answer during the time when everyone else was shouting out: Logic (I was juggling up between this answer and imagination - logic after all creates the orderly sequence of numbers that we know as positive integers and otherwise) Will be interesting to see what the rest of the video shows haha great stuff :-)

[@lawrencepsteele]

I was thinking along similar lines. My answer: rules.

[@factsverse9957]

I think that too, in fact when you prove things you don't use sets. Especially proving mathematical logic and stuff. His title is not technically true since he wrote "all mathematics".

[@andrewprahst2529]

I would say logic must be applied to something for it to become math, so I wouldn't call it a building block. It's like the mortar rather than the brick. Of course you it's what allows you to build, but it's not the thing you're building with.

[@krishields2]

@@andrewprahst2529 I would disagree, slightly. Logic is inherent. It need not be applied to something for that something to manifest naturally and systematically. Logic is what allows us to distinguish this from that, label and categorize them. You are correct in that logic isn't a building block - but it is the fundamental process that allows us to understand what the fundamental building block might be. To me, it's zero and I also consider zero = infinity.

[@iwbth7955]

the whole goal of division is to subtract until you get 0. if you subtract by 0, you wont be able to change anything and be unable to reach your goal. thus anything divided by 0 should be classified as "you're missing the point" and 0 divided by 0 equals 0 because you're already there.

[@manykoalas2735]

I'd have thought that 0/0 is still undefined, because you can take an infinite number of zeros away from zero and still have zero, so the fact that you're already there doesn't change the fact that dividing by zero is impossible.

[@johnwalker1058]

I would say that division by zero is undefined due to the definition of division and the definition of zero. Division is to break up or divide a number by another number. Zero is a number that represents nothing. Dividing by zero is to divide by nothing, which is essentially trying to divide by not dividing, since dividing by nothing is the same as not dividing in the first place. Thus, division by zero, by he definitions of division and zero, violates the law of non-contradiction, which is one of the key logic laws that mathematics follows.

[@iam1nerd]

I wish i had a teacher like Eddie when I was in secondary school

[@russellmorland7382]

Multiplication is the set of pairs of one item from the first set and one from the second. Division I haven't figured out yet.

[@Deswilkie]

Wish maths was taught like this when I was at school. I've paid more attention to this guy than four years of high school.

[@WalterHolokai]

You are good Eddie! Cool too but a great teacher.

[@khodanitshivhi3429]

Eddie im a young mathematician i really enjoy your way of teaching if possible i will like to attended one of your class

[@IeagueofIegends]

I think the more you know abstract algebra the better this video is

[@laocoste4966]

Mind blown!!

[@DudeJustWhy]

my answer was add and subtracting, because no matter what you use, real numbers or imaginary or even letters, the thing that makes math math is the interaction between those elements. and adding and subtracting seem to me like the most basic one, all the other actions like dividing or multiplying are made from them.

[@afzalthenotorious5956]

Hey , Eddie , could u plz upload the full lecture of this part...??

[@coldwynn]

It's called Subitizing. After that, addition (combining sets) and multiplication (sets of sets). From there, we just make crap up as problems arise to remain consistent.

[@skaterandrew]

Sets wow. I was thinking about value. This guy is awesome.

[@taleandclawrock2606]

I always thought maths was built on and about relationships. When i was little, numbers were alive to me, i saw maths questions as a beautiful multiple dimensional reality ( that literally looked to me like a bluish spece in constant motion, from which all could be derived and brought into focus and harmony.) I was always correct on my work. Then my grade 3 teacher, a grumpy womanwho never smiled,tookpleasure in publically humiliating me because i didnt follow her methods on paper. And i became phobic about maths. This is the first time since then (and i am 51) that i have enjoyed maths.

[@fbiagent6456]

Because methods are much more important than you think. Of course there are multiple ways to solve a problem!! BUT classical education requires mastery of multiple methods and not just one which was the most comfortable for you.

[@lorax121323]

@@fbiagent6456 Properly understanding math requires knowing how different methods should arrive at the same conclusions if they follow the same set of premises. If they arrive upon different conclusions, then it indicates that they differ in their defining axioms. The point of traditional education is the dissemination of one set of facts and at least one definite way of dealing with them, regardless of whether or not students can even conceive the possibility of other methods existing.

[@sentinel5943]

That girl from 15:45 it's me in every class when i finally understand something LOL

[@sahilsihol1317]

Oooh.

[@AgentOccam]

Same. I actually had the same reaction (but with my inside voice) and it was so funny to hear. Not because I didn't get negative numbers so much as just that way of showing the 'weird' negative result of an arithmetic operation can be rearranged into something that looks perfectly intuitive and routine to most people - but *it's the same thing.*

[@razuahmed1977]

1.digits 2.symbols 3.relation 4.logic 5.pattern 6.imagination

[@theevolutionaryalgorithm5947]

Other answers I have by the 12:36 mark (so still waiting for the rest of the video to finish) include maybe one of the following if not logic or imagination haha: (1) relationships (2) patterns (3) categories (4) abstraction

[@RadiantSharaShaymin]

My first instinct was indeed numbers, but then I thought it was 1, with everything being derived from the concept of 1. Then I thought it was definition (since 0 didn't seem to fit in with that) - using numbers to specify/understand something, like distance or an amount of time, and how they interact.

[@sednaahmed6432]

Woohoo what a great teacher

[@samwise8333]

In mathematics, take any question there is four things happen plus, minus, division and multiplication. Even multiplication and division are shortcut of addition and substraction.

[@gonzogil123]

Might even be able to say: just like we use words, we may use these other, names/words?, and put them together in different ways to say certain things? A possibility perhaps. Words are as empty, or, grammar structures are very much like algebraic variables, but more familiar to them.

[@umeshkad7091]

good teaching sir

[@Holobrine]

I think the basic building block of math is the concept of a whole, or one. Numbers arise when you need to keep track of more than one, operators arise when you start thinking of numbers abstractly, and new kinds of numbers arise when you start thinking of operators abstractly.

[@danv2888]

I would say that sets breaks down to counting, then comes "Haves and Have-nots." Which can be presented as 1 and 0. Now all are operations stem from counting. So addition use counting of the sets, and subtraction is the opposite but still is counting. Now multiplication is faster adding which goes down to counting. Then once again, division is the opposite but is still counting. If you want you can include any operations, and they will break down to counting then too "Haves and Have-nots." One more example is exponents, which is faster multiplication and it breaks down..... Now the opposite would be roots. This is the whole computer world 0 and 1.

[@NANA-yh2wx]

I wish I had a teacher of any subject like Mr. Woo

[@midwestrailroadproductions8116]

Hi Mr. Woo. You're right. There are many different origins of mathematics and science. For example, what's the basic building block of a computer. You start to tear it apart, and you find various circuit boards, such as the CPU (central processing unit), input, output, memory, storage, operating system, etc. There are building blocks of everything you see, such as computer software. If you dig deeper into it without using a scanner or an x-ray, you'll find binary code, which is the basic building block of computer software.

[@daviddemar8749]

This video got me thinking about a lot of abstract math -related stuff which I'll omit here. I never expected that this video would trigger such a mind-gasm (inspiration). I'd really love to see how he tackles division by zero. What a great teacher. I wish I could give him positive infinity likes 😁

[@b43xoit]

Usually "division" refers to seeking a single solution to an equation y = mx where y and m are given. But if y and m are zero, there is more than one solution. So seeking the single solution, you don't find it. So, no success at division.

[@daviddemar8749]

@@b43xoit Bravo !! I haven't been on a math binge for a while- but since I'm stuck at home because of Covid-19 ( new York State is under a stay at home order.) maybe now would be a good time to dive back in. ...

[@b43xoit]

@@daviddemar8749 What I, having been a poor student of the calculus, found most fascinating to learn recently about math was that of the simplest case of quantum mechanics that can be described, the spin on a single electron. Leonard Susskind lays it out it in KZbin posts from Stanford University. Quantum mechanics (QM) is a mathematical procedure that allows to predict the statistical outcome of repeating an experiment on a quantum system many times. When you measure the spin on an electron, there are only two possible results, spin up and spin down. QM says, given the angle you measure it at, the probability that the outcome will be spin up. To understand the math of this simplest case, you do not have to know any of the calculus. Just a little matrix arithmetic and complex numbers, but Susskind explains all that, for an audience who may have forgotten. And the notation used in QM is cool and abbreviates quite a lot with a few symbols. For example, if you see something like |a>, that's pronounced "ket a" and it denotes some column vector i. e. a matrix with just one column. And . Multiply a row by a column and you get a scalar (i. e. a single number).

[@daviddemar8749]

@@b43xoit Sounds fascinating I'll have to check it out. However I have confess that my understanding of QM doesn't go much beyond knowing about the double slit experiment, schroedinger's cat and knowing about the macro conflict between QM and classical Newtonian physics. This does put me way of the vast majority of the American population and only bc I'm blessed to be an alum ('78) of the Bronx High School of Science .

[@b43xoit]

@@daviddemar8749 Even though that particular series from Susskind is really an elementary introduction to QM, the title indicates that it is about entanglement. And he does eventually get to entanglement.

[@zoetropo1]

Events are the basic building block of special relativity. Binary numbers - equivalently, Boolean algebras - constitute the basic building block of mathematics - including logic and category theory (even of non-binary logic)!

[@travisbaskerfield]

An atom is the smallest fragment of a given element. It can not be divided into smaller fragments of the same element. So the word still orks as a definition.

[@cikguilyas]

i love this

[@tommasogiancaterino8188]

They way the class goes “yesssss” when he writes on the board division by zero, tells you a lot about the kind of teacher he is! Gj mr woo

[@mohakchugh1058]

Although... Would u consider shapes like triangles, circles and squares or even 3d shapes like cylinder, cube and sphere as symbols?

[@RockBrentwood]

Hey Dr. Woo! I got an idea. Let's make 1 the building block of *all* of arithmetic! We'll make everything else from it with a single operation - perfectly suited for balancing accounts - that we call "take-away", and denote it as "−". Every number, we shall decree, can be formed from 1 by taking combinations of take-away operations with it. We will impose two conditions: (a) for all numbers a, b: a − (a − b) = b, (b) for all numbers a, b, c: a − (b − c) = c − (b − a). We'll *define* the number 0 as 1 − 1 and call it the "break even" number. We'll then *prove* as a theorem that (c) for all numbers a: a − a = 0. Proof: a − a = 1 − (1 − (a − a)) = 1 − (a − (a − 1)) = 1 − 1 = 0, by applying (a), (b), (a) and the definition of 0. We'll *define* the "take-away" of a number as -a = (a − a) − a and use the theorem to prove that 0 − a = -a. Then, we'll define the *sum* of two numbers as a + b = a − -b and ... with these definitions ... prove that we have *all* the basic laws of arithmetic for the operations of plus and minus. For instance, a + 0 = a − -0 = a − (0 − 0) = 0 − (0 − a) = a and 0 + a = 0 − -a = 0 − (0 − a) = a ... using the axioms and results proved up to this point.

[@ChemistryEssentials]

What makes up Math? The equilibrium around numbers such as Pi, i, and e. Numbers are units we made up, but in the end it's just a balance of the numbers around equilibrium to come to an answer.