Is Zero Even? - Numberphile

[@iammaxhailme]

"I want to buy no sheep, I'll give you no pounds" That's the old school version. The 2000s version is "I want to buy no sheep, I'll give you no pounds plus a 10 pound processing fee".

[@nathanilemiller7750]

What

[@nanamacapagal8342]

Monthly

[@deamonsamurai9760]

and another 10 pounds for wasting my time

[@puppetsock]

If you don't understand "zero" I am not going to let you drive my car because you won't put gas in the tank. I'm pretty sure that farmers that over-wintered animals understood "nothing" as well. The stockpile of food for the animals and the other stockpile of food for the humans could get empty before spring. That would be a horrible disaster for the people depending on it. They either understood "running out" or they died. I don't believe this "didn't have the idea of zero" stuff. And empty plate, and empty cupboard, an empty barn, all of these were just other names for nothing.

[@justsomeguy892]

@@puppetsock they obviously knew about nothing, but not in the mathematically useful sense, that's all.

[@CaJoel]

The lack of ink in the marker deeply disturbs me

[@ClickClack_Bam]

I'm ok with it because it's evenly out of ink in proportion with the level of ink it has.

[@realeyes8199]

*deeply*

[@ratoim]

"I find your lack of ink disturbing."

[@azzteke]

@@ratoim Why repeat?

[@CarbonRollerCaco]

That's how it should be with this topic: near-zero.

[@romanr9883]

that makes zero sense

[@Proximity94]

+Walwalkn Wewnrkl Lol, I can't even...

[@samielsayed7445]

+Proximity94 so zeros the odd one out kek

[@TheLATbru]

You mean that makes even sense

[@starknifez4846]

That's a very odd pun, even for me...

[@christopherellis2663]

It is very odd, that nothing is even, whereas something might be odd, or it might be even. 0/2=0/3, IF not please demonstrate.

[@TroutOfOrder]

I remember as I child someone in school told me that there are numbers less than zero, and I almost didn't believe them. They said "yeah, they're called 'negative numbers'" and I was in shock

[@nickwilson3499]

Makes sense since negativity is basically just an abstraction. There’s no such thing as a negative number in our natural world.

[@mcvibing2785]

@@nickwilson3499 I cant have negative 6 sheep, or negative 10 apples. the closest thing would be debt

[@nickwilson3499]

@@mcvibing2785 exactly what I was saying. Debt is just saying “when you have more sheep, give some to me.” It’s just in your head, it doesn’t actually exist.

[@mcvibing2785]

@@nickwilson3499 yeah

[@BPEREZRobertJamesL]

F=-kx is Hooke's Law. What do you say? Oops, it's just a model.

[@DanZhukovin]

So zero is even. If you think zero is not even, then I cannot even, because that is too odd to believe.

[@novaryx]

bruh

[@stylus59]

Pass the blunt

[@anandsuralkar2947]

Hmm

[@user-bb5bf2tp4w]

odd + odd = even (3+5 = 8, 7+11 = 18), 0 + 7 = 7 (odd!)

[@avantika505]

@@user-bb5bf2tp4w I think it only works for natural numbers

[@nerdbot4446]

I once bought 0 sheep for 0 pounds. It made no sense, but it worked!

[@ricv.8015]

I do it all the time actually

[@sciencmath]

It didn't make any cents, either.

[@White-ul3dl]

I see this comment posted 2 years ago, the first reply 2 weeks and the second reply 2 days Therefore 2+2+2=6 My comment will be posted 1 second ago, the time it takes to refresh the page and find this comment again would be 5 seconds 6-(5+1)=0 0 is even

[@Ghost____Rider]

You bought it from 0 farmers

[@jocabulous]

that's pretty odd

[@ark9959]

You don't have to use a telescope to film your videos

[@northshorebuilt6364]

100 likes and not 1 comment. nuff said

[@person8064]

128 likes and not 2 comments. nuff said

[@Thebiggestgordon]

137 likes and not one person with a sense of humour. Nuff said

[@jamespolland958]

144 likes and no cats :( nuff said

[@Ahmet-fg4ul]

196 likes and no jokes. Nuff said.

[@fingernailclipper2152]

"0. That's our friend." Same [Insert sad violin music]

[@omikronweapon]

Hello Zero, my old friend.

[@benedictifye]

One, is the loneliest number

[@hamster8706]

0. Thats our friends 0 thats our friends Points give you friends

[@justclosing]

My bank account is even. It sounds better than saying you're broke.

[@trunc8]

Hahah

[@007RAJKOify]

Its better then being in dept though.....

[@justclosing]

-100.000 is even, or not?

[@PongoXBongo]

Even and negative.

[@FirstLast-fr4hb]

but its not negative, its zero. Negative is less than nothing.

[@aramoticy]

This is the first time I've heard a bunch of Brits use the word "zero" so often. Usually, I hear "nought"

[@pendlera2959]

You mean zero is naught so common?

[@zappycrook1130]

24kGoldenRocket stfu

[@Darklor_WCF]

@@24kGoldenRocket zed refers is an alternative pronunciation of the letter z instead of saying "zee"

[@TC_83]

IronCoreGroup “zee” is the alternative pronunciation, not “zed”. The entire English speaking world says “zed”.... only the Americans say “zee”

[@seabassthegamer6644]

@@TC_83 Which pronunciation is alternate is relative. That's not special though, just about everything is relative.

[@scottpoet]

I find it odd that we are even talking about this.

[@AClarke2007]

+Dylan N Ha ha ha, I even find it odd too.

[@Salarr]

Even I find it odd!

[@loekvanvucht8274]

Hahahahahahah

[@tubular618]

Even though it makes zero sense?

[@anandsuralkar2947]

@@TheGoatDyl even too

[@sarahb2425]

0:01 me on my maths results day

[@Surusmadness]

Looooool😂😂

[@explainedwithgpt]

underrated comment !

[@Thaplayer1209]

I found it odd to call 0 even

[@Tocaraca]

lol

[@CJBurkey]

I found it *odd* that you would _even_ bring that up.

[@KishoreShenoy1994]

Even so, you have to do so

[@benwaffleiron]

Que laugh track

[@aidanmmulv]

Ben Waffle queue*

[@briannalove749]

I honestly always thought zero was even because of when I was like six and we would line up in pairs at school, I concluded that zero was even because odd numbers always have someone left out with pairs, but even numbers don't, and since 0 doesn't have anyone left out it must be an even number. Now that can just be said as "divisible by two"... I love the way my brain worked

[@michaelhanford8139]

Brilliant! ...all i got from pairing up was traumatized🤷😆

[@PC_Simo]

@Brianna Love Well, in Finnish, the word for ”odd number” is: _”Pariton Luku”_ (lit. ”Pairless Number”), and for ”even number”, it’s: _”Parillinen Luku”_ (lit. ”Paired Number”). 😅🇫🇮

[@PC_Simo]

@@michaelhanford8139 Like getting picked last to the team, in PE.

[@pepe6666]

@@PC_Simo you can be pair with ...the teacher! ...:( thats me at school

[@PC_Simo]

@@pepe6666 It could have been me, just as well; and probably would have been, if being pair with the teacher had been a thing, for us. My sympathies. :(

[@SternLX]

When he mentioned Divide by 0, I immediately imagined a spread sheet covered in #DIV/0!

[@Mullkaw]

you poore soul

[@coleabrahams9331]

I imagined a y=1/x function and how there is an asymptote at x=0

[@PiyushSharma-hy2ej]

That's 0!, so that will work cause it's 1

[@Liggliluff]

I wouldn't have a delayed reaction if someone asked me if zero was even, and this video helps me be even more sure about my answer. - But I might be the odd one out.

[@li_ka2]

I think I would have. Zero is a weird number that kinda follows it's own rules (you can't divide by it, anything multiplied by it is zero, stuff like that) and if you're asking me that I will assume you're tricking me (like asking "is a banana a berry") Ps: swede?

[@ssgoko88]

0 is one less than a non-even number. Ergo it has to be even. Wheres my nobel prise.

[@elliotgale470]

7 is less than an infinite number of non-even numbers. Ergo it has to be even. Where's my prize?

[@elliotgale470]

***** exactly, thank you for noticing

[@ButtonMasherReal]

2 / 2 = 1, so 2 is even 10 / 2 = 5, so 10 is even 0 / 2 = 0, so 0 is even The pattern is that they all become whole numbers when divided by two. Nobel Prize now.

[@seangrand3885]

Doktor Karlos Mathematicians do not get a Nobel Prize, you know...

[@PsychShrew]

Elliot Gale He said ONE less.

[@jangofet555]

1 2 4 8 7 5 what do these have in common? what does 3 and 6 have in common? and why is 9 the only number that always reduces back to 9 from multiples of it self? ie 9x4 = 36 3+6=9 or 9x52743=474687 4+7+4+6+8+7=36 3+6=9.

[@invalide]

Is zero even what?????????? It's 3 am and I haven't slept in a day

[@invalide]

tephine 726 ???? Wat ????

[@199022009]

Zero can.

[@nicolasanese6499]

This comment is odd.

[@want-diversecontent3887]

MrBlueSky Is zero even a number divisible by two and can be added by two numbers and can be added with another number that is not divisible by two and become a number that is not divisble by two?

[@SPFAlpha]

Invalide_Account meth... helluva drug

[@MonsterTeegs]

Magic the Gathering players: I've been training my whole life for this moment.

[@mn6334]

I was about to make a similar comment...

[@BarginsGalore]

*void winnower has entered the chat*

[@thydevdom]

I don’t play but I’m curious what you mean with your comment. Lol. Care to explain?

[@BarginsGalore]

Dominik Brame some magic the gathering cards reference odds and evens and on every card that mentions them they say that zero is even. It’s kinda become a joke I’m the community

[@Dexaan]

(Zero is an even number)

[@Sjackson2369]

Another thing you could say is that two odd numbers added together will make an even number, but when adding zero to an odd number it remains an odd number

[@harleyspeedthrust4013]

"I feel like the answer is no but it feels like it is because it's round" Secretly, we all feel the same way

[@narcoleptic8982]

Question: Is zero even? Answer: No, it’s naught.

[@kourii]

*nought

[@glebkachur8033]

shut up, dad

[@yingo4098]

i'm gonna give u pun-ishment

[@Blaze42069-z]

Makarputo

[@victordatsiuk]

One of the best jokes i've read👍

[@Liggliluff]

Brady's logic to even numbers, if they're round. So let's list them: Even numbers; 0, 3, 6, 8, 9 Odd numbers; 1, 4, 7 2 and 5 are both odd and even; Odven? Evedd?

[@akberjag]

8 is even EVEN..

[@oz_jones]

@@akberjag even Steven

[@MrAffeman]

If you have nothing, nothing it is, but something put in front of nothing makes something that has nothing behind it.

[@Farmeryeti]

I thought 0 being even was common knowledge? And I'm awful at maths.

[@MasterOfTheChainsaw]

Farmeryeti I think that most people intuitively thinks of 0 as even, but after learning more about 0 and how it acts in a weird way in many cases, like how 0 is neither positive nor negative, and how you can't divide by 0, some people might start to question whether 0 is actually even or if it's neither even nor odd. Apparently it does fit in well with the even numbers though.

[@jonathanpark4619]

MasterOfTheChainsaw It's because even numbers are defined as anything that is equivalent to 0 mod 2. Nothing really deeper than that.

[@jonathanpeck]

Jonathan Park Somewhere in the galaxy, we have the same name!

[@jonathanpark4619]

Jonathan Peck !!! Hahhaa

[@columbus8myhw]

Farmeryeti My sixth grade math teacher didn't know this. I was very surprised.

[@Sovnarkom]

I have $0. Must be the devil's work.

[@hienduongvan8454]

this must be the work of an enemy stand

[@ifrazali3052]

Lol

[@Bartooc]

Not even odd at all.

[@markusjacobi-piepenbrink9795]

"Is zero even … a number?"

[@neverrip6809]

Nope.. it's sort of not a number... -1, -2, -3 are counting backwards, +1, +2, +3 Is counting forward.... 0 has neither a + or -. Zero belongs at the start of an equation like a capital letter ie 0+6/+2+(0+1+2)= 0+1. I'd say people have lost their mind with maths, but maybe they never had it.

[@cgiunta6542]

Yes, according to my programming language.

[@neverrip6809]

@@cgiunta6542 yea, der, I know. Binary code is different to maths. I stick to maths tho.

[@sandeepbannore4185]

@@neverrip6809 zero is a number.

[@amzwl1671]

Alex Prangnell / Binary is a base 2 counting system. It is still very much maths haha

[@lomax343]

Slightly at a tangent, grammatically-speaking zero is plural. Consider - "There are two cups on the table" - Plural "There is one cup on the table" - Singular "There are no cups on the table" - Back to plural

[@anon3988]

This is relevant how? That is a grammatical caveat and nothing really to do with maths.

[@lomax343]

I did say I was going off at a tangent...

[@micahvalentine4878]

+lomax343 Grammatically speaking, so are decimals. on average, households in the US have 1.7 toasters.

[@Oxy456]

There is no cup on the table.

[@Deluxeta]

That implies there was supposed to be one.

[@wethdtdi]

i dont understand much about math, but i think looking at the numbers that even number is a number between two odd numbers.. so 1 and -1 are odd.. 0 must be even :)

[@stevenhorsley5194]

Thank you I was gonna say that

[@davidmurray3542]

This was my thought as well.

[@omikronweapon]

three people that didn't bother to watch the entire video?

[@anaunaga5471]

My favorite number is 8 because it can be divided physically and mathematically, and can be cubed

[@kylebrainpresents]

PiZzA ZiZa wait what is 7 a common favorite number?

[@anaunaga5471]

***** 8 just has that special feel to it, and it is a common number in computing

[@abadlydrawnsnowman1648]

My new fav number is -1 because e^iπ=-1

[@GhostInTheShell29]

My issue with negative one is its root is imaginary. And something tangible coming from something imaginary :p causes a lot of headaches in a philosophical sense.

[@jmcwd]

My favourite number is 256, because it is 2^8, or the amount of numbers you could have in 8-bit binary.

[@noahburns6042]

Also, algebraically, an odd number is a number that gives a whole number when doubled and minus or add 1: 2n-1 is odd, and so is 2n+1 Let's say, for 0 to be odd 2n - 1 = 0 2n = 1 n = 1/2, but because n in this case isn't a whole number, in fact halfway between, 0 can't be odd, so is even. Moreover, using the same calculation, an even number will always be something and a half, for example 2n - 1 = 2 2n = 3 n = 1 and 1/2 2n + 1 = 10 2n = 9 n = 4 and 1/2

[@waffleless]

*draws a wide circle* "Zero!" ... You what?

[@avi8aviate]

It's a 0 on its side.

[@gioschrijver5683]

Not positive nor negative. Neutral?

[@emmanuelalbazi8560]

Yup.....

[@Rajsadaye]

Yes!

[@TheGeneralThings]

Technically called unsigned.

[@pavankmanjithaya]

or has both signs

[@leofisher1280]

Cody Griffin it is most certainly not called unsigned

[@KaitouKaiju]

Zero literally can't even

[@AveLudusMagnus]

I just came here to make that joke, but you already did. Thanks

[@shadycharlotte9144]

SentsuizanXS Actually it literally can't odd.

[@anandsuralkar2947]

It makes me feel odd

[@ShelliLoop]

Does your native language have "odd, even, zero...."? I think you are buggering English. Try rewriting your comment so it makes sense?

[@danithegoat1416]

I am the 666th like

[@ArgyleAdams]

For base 10: Every number with an even digit in the ones place is even. Every number with an odd digit in the ones place is odd. Every number with a zero in the ones place is even. QED zero is even.

[@stumbling]

Does zero even even?

[@transformersloverjon]

CowLunch No!

[@Rhovanion85]

CowLunch Eventually maybe

[@007tene]

+CowLunch do you even even bro

[@lovrocroatia2]

+CowLunch That's Odd

[@-danR]

Well, I've never read it.

[@MrJonndoe]

1:50 a little correction, Al Khorezmi was the founder of modern Algebra and algorithms. The word Algebra is taken from this scholar, and he was not from North Africa, he was from Central Asia. Khorezm, which is currently in the territory of Uzbekistan.

[@drshafat4219]

Came here the guy who believes books came from SKIES

[@nicklang7670]

I love this video. To know the number zero was causing people who abuse power to lose power over and over and the story of zero becomes a great historical philosophy that needs to be told well!

[@WtbgoldBlogspot]

Just so y'all know, the word for "Fiveness" is quincunx.

[@EchoHeo]

WTBGold Kwingcungs

[@MunkiZee]

No, it's an abstract idea

[@jaspermay5813]

Quincunx means 5/12 of an inch (uncia) or the pattern of 5 dots e.g. on dice. I think a Latinate word for 'fiveness' could be 'quinquity'.

[@gianfrancoAA]

No

[@oz_jones]

No it's not. It's _fiveness_

[@antimaster6432]

can you guys explain the fundamental maths on sin, tg, cos and ctg?

[@prateekgurjar1651]

they are just ratios...and I guess it would be a boring video

[@DommHavai]

Wiki can reveal this mystery for you.

[@prateekgurjar1651]

Thinking again, that would be a nice history video if they show how they were developed.

[@coolguy284_2]

(tg is usually abbreviated tan) i mean, they are all related to the x and y coordinates of points at a specific angle on a circle (sin and cos) and on a tangent line that intersecs the x-axis(tan and cotan)

[@angelmendez-rivera351]

coolguy 284 If you are talking about the modern definition, sure, but the historical origin is far more complicated than this. In reality, what happens is that you draw a circle and then a triangle using a central angle. There are many limes that have some special relationship to the circle, e.g a tangent line or secant line. The ratios are then defined in terms of how the special line is parametrized by the angle and the radius of the circle. Only a few of these ratios are taught today, though, which are the sine, cosine, tangent, cotangent, secant, and cosecant.

[@Rhovanion85]

6:12 This is interesting. As a software engineer who uses Oracle databases you actually have a value called NULL which means "nothing". If a value is NULL it acts completely different when used in operations than a value 0, which is numeric. A string of text for instance that is not saved can be NULL, but it cannot be 0. Multiplying by NULL also returns NULL , like zero, but If you add a value to NULL you will also still have NULL. If you divide by NULL you will have NULL as well. in logical operators such as "equals to" it gets even weirder. if you have a branch in a function for instance "if variable = NULL" the expression will alwayus be false, even if the variable contains value NULL. if you have 2 variables, and both are NULL and you ask "if var1 != var2" (!= means "not equal to") it is also FALSE. an operation with NULL does not only always return NULL, it is not even equal to... itself.

[@Lhorez]

Null as implemented in many programming languages doesn't mean nothing. It means (essentially) "I don't know". That's why nulls propagate. A simple example: If I say "1 plus something equals what?" You'd probably ask "What is something?". I'd shrug my shoulders and you'd then say. "I don't know." 1 + NULL = NULL. Multiplying or dividing by 0 is a bit trickier though so the explanation isn't as clean as this.

[@HDitzzDH]

I always thought it was obvious that 0 is even, if you have an even number and subtract/add 2 your new number will also be even, so if we start at 8 which is even, then subtract 2 = 6 (even), subtract 2 = 4 (even), subtract 2 = 2 (even), subtract 2 = 0 (even?)

[@skpcboy]

1 is odd, 1 + *2* = 3 3 is odd, and... 2 is even, 2 + *2* = 4 4 is even, so.... 2 - *2* = 0 simple theory :)

[@MrAffeman]

Zero is a representation of nothing. But nothing can be something with something in front of it.

[@Liravin]

6:13 it would make more sense to me if he finished by saying "nothing is when there's nothing to count - zero is the absence of something"

[@bobwilson7684]

nice one, clever

[@simonflorey5428]

They say money talks , but all it has ever said to me is goodbye.

[@jonathan3504]

Al-Khwarizmi (or Al-Juarismi) was not established in North Africa: he lived and worked in Bagdad in the IX century and is mostly famous for his compilations and contributions to Algebra (he gave its name to this branch of maths) and Arithmetics among others.

[@shaamyl6856]

If you are not an Indian and not a Hindu, than how can you make such a funny comment :) No one stole anything from India, Muslim scientists were dominant in India as well sir :)

[@shaamyl6856]

Lol, wasn't a joke, it was the truth, you can research the timeline quite easily

[@arjungajra684]

__I__ haha

[@mridul303]

+Shaamyl Anwar Islam came to India at around 700 AD. Aryabhatta used 0 as number at around 500 AD.

[@shaamyl6856]

Yes Mridul, I never talked about the use of 0 only, just Al-Khwarizmi's contributions to Maths generally

[@sereysothe.a]

CORRECTION: al-khwarizmi was from modern day uzbekistan (then part of persia), and he did his studies in baghdad

[@columbus8myhw]

***** He even said "Al-Khwazimi." Which sounds... weird.

[@mustafatalaeezadehkhousani4856]

namn Just to add that we have "Algebra" thanks to his works in this field and unknowns (he'd call them Filān_x_ and Bahmān _y_) in his book Ilm al-jabr wa'l-muḳābala.

[@listocalisto8124]

The persians found out a lot of things of todays science

[@sereysothe.a]

Shashank Jaiswal well, khwarizmi didn't claim to invent anything. but instead his book was an in depth study that used greek, indian, and babylonian mathematics and *built on it with his own techniques.* also, while only certain rules of quadratic equations were defined in india and greece, it was his book that clearly brought together the knowledge and set the foundation for what we have today.

[@sereysothe.a]

Shashank Jaiswal the real hero is omar khayyam

[@gdub454]

My friend asked me one time "What is one of the greatest discoveries?"...of course..I said electricity(which is an obvious one)...he then tripped me out with the discovery of zero...what is great irony w/ zero is even though by itself zero = nothing...put it next to a 1 - 9 #...and it makes its sum larger...that is the best case of irony I can think of...

[@kanakTheGold]

Loved how to topic progressed from Is 0 even a number? to Is 0 an even number?

[@michaelstrickland9736]

I've always seen zero as "genderless," unless a larger number ends in zero. Then the zero makes that number even.

[@Iam1nsane]

I have a question though. 0/2=0 & 0/3=0. So then, 2=3? I am saying this because that is how, division by zero aint possible and not equal to infinity was explained. Although keen at maths too, i have always considered zero as even but after watching this video, i am actually having some doubts. lol. Nice vid BTW.

[@justabunga1]

They are both to zero. The contradiction here is when you divide 0 by 0 since it's indeterminate. Anytime when you divide by zero, it is always undefined. Both of these statements when you get into calculus can be used in terms of limits. 0/0 is one of the indeterminate forms where you have to do more work using either algebraic method or l'Hopital's rule. 1/0 may have the limit to no exist or going to positive or negative infinity depending on the function assigned.

[@Mayhamsdead]

"Is Zero Even?" "When counting, is the number next to an odd number?" - if the answer is < yes > , regardless of what number you're talking about, the number is even.

[@Anklejbiter]

I like that they ended the video explaining the difference between 0 and NULL.

[@lisantica842]

I enjoy your videos. If zero is neither positive or negative, can it also be said that it is equally positive and equally negative?

[@andrestricker4118]

Bubbleonians. There are many reasons to love Numberphile, the accent is one of them. Thanks for explaining

[@casperv5270]

it always seemed intuitive to me that zero is even, because 0 % 2 = 0, after dividing it with 2 there is no remainder.

[@andrerenault]

I like the format of this and the root 2 video. Two different presenters giving different talks about the same topic, interwoven.

[@markdstump]

Well, zero IS congruent to 0 Mod 2, which would be my definition of "even." :)

[@kdbacho]

Mark Stump I think you mean 0 is congruent to 2 (mod 2), as congruence works like this, if a mod c = b mod c then a is congruent to b (mod c). You are right in saying 0 is congruent to 0 (mod 2) but it is also congruent to 0 (mod 3) or 0 (mod 5) etc. Just wanted to let you know :)

[@kdbacho]

Mark Stump Thank you for clearing up the misconception. I thought you meant if for all natural numbers x, if x is congruent to x (mod 2) than it is even. Now I see you meant if for all natural numbers x is congruent to 0 (mod 2) than it is even, which is correct. Although you could have made your definition even better by just saying if x mod 2 = 0 than x is even, which is the same as both your's and Brady's definiton. :) And I do think 0 is even because it is a multiple of 2. Its kind of interesting to see whether people choose division or multplication to define even/odd numbers.

[@markdstump]

Jeevan Devaranjan It's the same congruence class and the same set of integers! Still, you had me worried for a few seconds: I'm old and senile, but I know how it works. I'm saying if "a" is congruent to 0 mod 2, it's even. (My proposed definition) If you think this definition fails, show me an "a" that is congruent to 0 mod 2, but isn't even... or show me an even number that is not congruent to 0 mod 2. I said nothing about congruency to 0 mod 3, 4 or 5... if we did have the word "threeven," of course I'd want a similar definition and I'd want to include 0 again...so it'd be even AND threeven. This doesn't bother me; I don't think it should trouble you. Surely you don't think 0 should be considered throdd!?

[@arckocsog253]

In casinos, 0 is neither odd nor even.

[@AClarke2007]

+Arc Kocsog Casinos also use "00" too!

[@dongryeongkim9828]

+Arc Kocsog lol

[@kimjongdavidsothesexymugba1138]

+Warrior Son wtf

[@adamledger6836]

+Arc Kocsog this is correct

[@sanderd17]

+Arc Kocsog The only reason for that is to make profit for the casino. When you bet on even, and it's correct, you get to double your money. But there are 18 even, 18 odd and one zero on the board IIRC (37 possible outcomes in total). So if you put M euros on it, the average amount you get back is: (18/37) * 2M + (19/37) * 0 = 36M/37. So on average, you always get less back than you put into it, and the 1/37 left over is the profit for the casino. Another way to visualise it: say there are two persons gambling, one always puts €10 on even, the other puts €10 on odd. For most runs, the result would be even or odd, and the casino wouldn't gain or lose anything. But for on average 1 in 37 runs, the outcome will be a zero, and the casino will get the complete pot of that run. The only way to win with the roulette, is to not play it often. When you play it only a few times in your life, the final result will not get the chance to average out (and hopefully to your advantage).

[@SpectatorAlius]

The answer to the question is, 'yes'. Zero is an even number. Otherwise the set of even numbers would not be closed under addition (subtraction). Why he needed nearly seven minutes to explain this is beyond me.

[@galaxybounce1002]

Because the explanation is what people are interested in.

[@CinematicLaboratory]

Yes, it's the ultimate even number. Zero is the most important number in mathematics. It's the origin of the Universe. The here and now. The center of future and past. The only spot in the universe we can be absolutely sure about and we're always right in the middle regardless of where we think we are.

[@steveapplegate2425]

It would be interesting if you discussed how the Romans viewed zero and how they did calculations. I know they used the abacus, but what about paper calculations?

[@barthanson3043]

What is the Roman numeral for zero, BTW?

[@asb8686]

I never get to finish my math homework and I literally have never gotten higher than a C for math. Yet I do like to watch these videos

[@B3Band]

Is zero even what?

[@StrzelbaStian]

+Bloodbath and Beyond What is this? I don't even.

[@matthewlewiscomposer]

Of course

[@planetjanet3845]

+Strzelba Stian I can't even

[@yadroi]

Don't be a zero, get even!

[@justabunga1]

He is referring to an even "number". 0 is an even number. 0 is also considered to be both "even and odd function".

[@carolstott5337]

I love these videos. They make my brain hurt, yet I somehow understand them...

[@mizuhonova]

As the great Randy Savage once said, "Nothing is nothing". He was the cream of the crop.

[@davidm4547]

I'm with you on that. It's hard to pin qualities on nothing.

[@TheLOLSquad]

The addition of odd and even numbers is quite interesting as well. When adding any even number to an odd number, the answer is always odd. But adding any odd number to an odd one gets an even.

[@cloudybrains]

I can't even

[@gl1zzy999]

clickhead please dont

[@cloudybrains]

Ecto Don't even what?

[@General12th]

CLICKHEAD PLEASE DONT

[@cloudybrains]

***** But why can't I even? D:

[@GrandMaMaYT]

that's very odd

[@hubb8049]

Also, if you have an even number of negative numbers in multiplying/dividing then the answer is positive Example: 4*(-5)=(-20) because there is 1 negative number and 1 is odd (-7)*(-3)=21 because there are 2 negatives etc. 7*3=21 because there is 0 negative numbers and therefore 0 is even

[@spiewajit4ncz]

zero is dividable by two, so it's even. where's the problem?

[@factsverse9957]

Roulette

[@Kokurorokuko]

Aravind Suresh what that has to do with the topic?

[@spiewajit4ncz]

@lygophile That's correct, but what does it change? The number being even is not about ending up with 2. By definition, it's about being integrally divisible by 2. And 0 is.

[@larsmaurer6738]

@lygophile "isn't that an equally valid definition of 2, that it has a prime factor 2?" No. It's no equally valid definition because zero wouldn't be even then. ;-) "no even number starts with the letter "z" ... zero does!" - just joking :-) What is the correct definition for an even number? - It is divisible by 2. 0? Yes. This is the definition that can be found on Wikipedia. - It leaves no rest when divided by 2. 0? Yes. - It is a multiple of 2 and another integer. 0? Yes. (no prime factorization here....) What is the alternative? odd = not even (this is the literal definition) As all integers are either even or odd, then zero would have to be odd. even * odd = even .....will not work then. ;-) bad things will happen. fun fact... If there was a word for a number being divisible by 3 - let's say "threven" - zero would be threven, too. (Sorry for bad English, I don't think that automatic translations can handle mathematical subtleties.)

[@pashimanu0073]

@lygophile whether zero is even or odd??haha There is no point of arguing about it because zero is even by definition and not by any logic. For example, composite numbers are composite numbers by definition if the definition was like "a composite number has at least 1 factor(say)" then we would say that 0,1,2,..are composite. These rules and definitions are made by humans and not by nature 😂. @Lars Maurer has stated the definition of even numbers above. Read it. If the definition have any such point which you have said (can't divide it by any no. to get 2) then it will definitely be excluded from the list of even no.s

[@pranavlimaye]

This is such a great video, I can't even!!!

[@sergiomontecinos9631]

You should make a video about 1 being neither composite nor prime. (Don't know if I said it write)

[@1ToTheInfinity]

*right

[@mohammedyakub3760]

He made a video explaining how 1 isn't prime

[@scragar]

> Zero is neither positive nor negative In maths. In computing we have negative and positive zero for IEEE floating points because sometimes something is smaller than the smallest number you can express and being able to say "this number approached 0 from the negative direction" or "this number approached 0 from the positive direction" is helpful.

[@midassandahl5076]

Ive always learned that every second number is even so its always been kinda obvious

[@Bloodmoon17]

What the hell is with this thing about Babylonians and Greeks using a "space" to differentiate between the numbers 26 and 206? The Greeks used a alphabet-based numeric system, much like Roman numerals, but with the Greek's ancient alphabet instead. They often times used obsolete letters or isolated symbols instead. They did not write it like the numerals we used. With that, I can hardly believe anything else in this video, as a lot of it is based upon the whole "space between numbers" shite.

[@brendanmccabe8373]

Wasn’t Alqazeme from the Middle East also I apologise for misspelling his name

[@thehiddenninja3428]

Yes, Al-khwarizmi was indeed from the middle east, in the Persian Empire. His name is also the origin of the word "algorithm"

[@greedowins]

[@diarminator]

3:55 if you add 2 odd numbers together it's even

[@redsunrises8571]

3+(-3)=0

[@jasonlal9570]

@@rohitkunvar8881 wait what

[@AlexKing-tg9hl]

It’s a Parker even. That doesn’t make any sense does it?

[@DeathBringerBecky]

Nope. Not when its so clear cut even

[@Subpar1224]

Yeah that makes zero sense really

[@linkin543210]

No, he is a bit odd.

[@Will_tell_you_later]

Plot twist : they were explaining that "is zero, even a number".

[@FallofDarkness55-Resurrected]

If you divide by n such that n is a divisor and n approaches zero, you can only take the limit of that expression. For example, the limit of (x^2 - 1)/(x + 1) as x approaches -1 is - 2.

[@martinkunev9911]

Why would anybody be confused whether 0 is an even number?

[@branthebrave]

+Martin Kunev Because it has no value.

[@bengtbengt3850]

+Brandon Boyer 0 definitely has a value. If it wouldn´t, then it wouldn´t be defined as a number since every number has a value. Compare with for example 1/0. 1/0 has no value because its undefined.

[@branthebrave]

Bengt Bengt Do you even know anything about the basic history of numbers? A very long time, numbers weren't necessary for their basic lifes, but as time went on farmers could have been counting his cattle with tallys, and then civilizations started to use much more complex systems. One of them realized that to say that they had no cattle or no money, they would have to use the number 0. Some parts of the world didn't accept this because they thought the people who made it up ( I think Indians) were Arabic, and were their enemies at time, so Europe and some other places didn't use 0. The Greeks didn't use 0 because they didn't feel as if they needed it. 0 really does mean 'nothing' It's closes to nothing you'll get to. Btw I know this because I read a book about the history of mathematics.

[@martinkunev9911]

Brandon Boyer The arabic numbers were invented in India but came to Europe through the arab world. Europeans thought they are somehow evil because they came from the arabs and it was too easy to change the number drastically (falsify it) by adding a zero. Fibonacci was one of the main supporters of the numbers and popularized them in Europe. Hundreds of years ago people had difficulty understanding the concept of 0. I doubt any person without intellectual disability today will have trouble understanding it.

[@MrCmon113]

Yeah I never heard of that.

[@savannahritz3473]

Can you translate this in a third grade fashion ?

[@darksidecola4529]

0 is between 1 and -1 , which are odd, so 0 is even.

[@jawsome1185]

Also, 0/2 has no remainder. Odd numbers divided by 2 have a remainder. 0 has to be even then.

[@captainalkaloid5342]

When I was 8 years old, I always told people that.... They called me a madman

[@barryoffeastenders]

😂

[@cedricgist7614]

Thank you for not overwhelming me in this discussion!

[@masturboy8437]

That bald guy knows little about the history of math: he says that zero was banned by the catholic church because it was introduced by the time of the crusades, ignoring the well known fact that Pope Sylvester II (also known as Gerbert of Aurillac) himself introduced the arabic numerals in Europe (forcing the clergy to use them) more than 160 years before Leonardo de Pisa was even born. Also, Gerard of Cremona and Robert of Chester translated al-Khwarizmi's works several decades before the birth of Fibonacci. The first crusade started in 1096, when the decimal system had been already in use (not by everybody of course) for amost a century. Fibonacci was important in popularising this decimal system but was not the first and not the only (apparently merchants who dealt with the arabs were at least as important as intellectuals in getting used to the new system and importing it into Europe). I don't know what happened later but those stories about zero being banned in Florence seem to be related to local government and not the higher authorities of the Church (in which case it would have been banned in Rome or Avignon instead), i've also read that it was banned because of the novelty of the system which lead to suspicions of fraud and speculation. I don't know about that but all i can say is that Fibonacci is important enough to need any help from people adding legendary merits to his legacy. Fibonacci's Liber Abaci by the way does mention zero which he calls zephir (probably contributing to giving it its modern name) but wasn't a translation of somebody else's work though he acknowledged the contribution of arab and persian mathematicians to his own learning. I want to point out also that Fibonacci called the arab numerals "indorum" in that book, this means indian numbers not arabs, and we can find them called indian in many other old books and manuscripts, so it wasn't like everybody simply ignored that they came from India rather than from northern Africa. Also Al-Khwarizmi was persian, not from North Africa (though he was famous all across the muslim world so it was easy to learn about him while being in Egypt or Morocco).

[@smurfyday]

+Masturboy84 You should look up independent accounts before jumping to the defense of the Catholic Church. Copernicus, Galileo, and hundreds of thousands of "witches" later, and you still can't accept it has never been a front-runner on anything useful in society. I hate to say Wikipedia, but you should look it up before saying religious folks didn't try to ban 0.

[@masturboy8437]

All i am defending is an informed exposition of historical data which is something this video lacks. I know very well Galileo's life and also Copernicus' but i don't understand why you mention the latter since he was never prosecuted by the Church (the same institution that he belonged to). And even if he was that doesn't change any of what i've said about the history of the decimal system, which is what this discussion is about (we're not talking about astronomy). If you want to discuss my statements about the story of the use of the arab numerals please provide reliable sources that show me i'm wrong to say Fibonacci wasn't the first to introduce them into Europe or any of the other points i'm trying to make.

[@eugenecallahan1698]

Right: the history of Arabic numerals and the Church that Roger Bowley offers is complete BS: the Church never called them evil and they were introduced in Europe a couple of hundred years before Fibonacci. Wikipedia mentions nothing like what 'smurfyday' implies, and I asked a professional historian of mathematics about it and he said, "Yes, complete BS."

[@eugenecallahan1698]

Also, (I think it is Roger Bowley... not sure where I got his name, though) can't even be bothered to get auxilliary details right: the book he mentions was by al-Khwarizmi, not al-Khwazimi, and he was Persian, which is fairly far from "North Africa."

[@eugenecallahan1698]

@@smurfyday "hundreds of thousands of "witches"" It was thousands, and they were almost all burned by Protestants.

[@MrNutter]

Zero is infinitely zero.

[@twinkiesmaster69]

The 1 Realm of Retro! hi

[@MrNutter]

??

[@luispereira2354]

The 1 Realm of Retro! Hey How is it going?

[@851852093114208513]

...but CAN zero even?

[@justabunga1]

Yes, he is referring to an even number.

[@dharmendrkrishnia955]

If we multiply the equation ax^2+bx+c=0 by( -1) then here if we cosider 0 as a negative integer then there is no problem ! And if be consider it to be positive then also no problem so 0 should be both positive and negative hence it is placed batween the number line what do you think numberphole?

[@JackyRowe]

0:18 "£5, 20s" So £6 then...

[@KingFredII]

I fail to see the problem. I didn't need a split second: yes, zero is even.

[@EGarrett01]

All you've done is advertise that you're an idiot who clicks on videos that address things you already know.

[@KingFredII]

+EGarrett01 No, I click on Numberphile videos because they're interesting. You just called yourself an idiot by not understanding that obvious fact.

[@KingFredII]

+EGarrett01 Why not? He also said if you add up positive integers you end up with -1/12. Now one more insult from you and I'm going to report you which might lead to termination of your Google account. In other words: shut up!!!

[@EGarrett01]

Now that I've pissed in your cheerios, buh-bye.

[@Heligoland360]

+EGarrett01 Well that was a pleasant conversation.

[@bobmichaelsen2891]

Zero is even! Just look at the reminder text of Void Winnower! (MTG Joke)

[@thedarklight6752]

wow

[@SuperKako17]

Please don't explain the reference when making geeky jokes. The whole point of it is to make it funny only for those that are worthy.

[@cryptokami]

What ever number/counting/completion system you use, zero is always the higher receiver in the system, while it's higher emitter/receiver completon changes as we change our counting system. (Completion - the digital sum of all the numerical elements in the number system. Completon - two numbers, one of each type(emitter and receiver/odd and even) that add up to make the completion.)

[@abdullahenaya]

I've always considered 0 as even

[@frankdipaulo655]

When i saw the title, just thought "is zero even, WHAT ArE YoU HiGh?" lol!

[@brianhanson9367]

All I know is, nuthin from nuthin leaves nuthin. Billy Preston.

[@Randsurfer]

You gotta have sumthin, if you wanna be with me.

[@JayTemple]

At Billy's funeral, one of the tires fell off the hearse. It went round in circles.

[@MichaelClark-uw7ex]

If you subtract an even number from an even number, the result is always an even number and if you subtract an odd number from an odd number, the result is always even, so, for example, 2-2=0 and 1-1=0, also we know 0 is a number; therefore, we can assume that 0 is an even number.

[@Diedela]

This was literally a question on my test

[@PhillipAmthor]

Did you pass?

[@Diedela]

It was considered to be even, and I got it right. But after a whole lot discussion in class after the test, I think they gave the others half a point.