3 is everywhere - Numberphile
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- Опубликовано: 2 июн 2024
- Almost all numbers contain the digit three - and we can prove it!?
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Soooo basically, "Almost all numbers contain almost all numbers..."
+Mirage Uchiha Almost all numbers contain ink, toner or absence of light.
+Mirage Uchiha -No-, it's: almost all numbers contain any one chosen digit. :P Intuitively obvious if one realizes that the longer the numbers are, the more digits they contain, and the more chance for a random huge number to contain your chosen digit.
Bah, and yes, you're obviously right - when looked at it for more than five seconds I spent writing the comment - yes, almost all numbers contain any chosen number. Because infinity. :P
This doesnt make sense, i mean not what you said but what the video says.
How can there be 3 in all the numbers based on the result being 1? If the result is 1 does it mean that the numbers which do not contain 3 is 0? Thats impossible because the sum of number which contain 3 and which do not contain 3 is supposed to be 1.
LotusEater Not in all numbers - in almost all, as in - the larger the number, the higher the probability that it contains 3, and it tends to 1.
And it's the reverse - probability of a number not containing 3 tends to 0 as the number grows.
Tomasz Wota
LOL how can the number not containing 3 tend to 0? there are always more numbers not containing 3 than there are numbers containing 3.
Thats the whole point about the answer 1. That answer 1 is totally WRONG if the sum =1.
The combination of numbers 18492833949283792749192829323000023934823 is also in almost every integer. What a wonderful thing infinity is
This April fools joke got me too
+Sergio Cordova He's not wrong because infinity
infinity is wonderful OR mathematical profs are almost worthless.
Oh boy, you made my day!
That was the first thing come to my mind ;)
It sounds surprising at the beginning, but formulated the other way around it's more obvious: "the probability of any given number to NOT contain 3 goes toward zero".
ooooh yes, I was wondering how is it possible that the same thing applies to all numbers from 0-9, but this makes sense now haha, how come I didn't see that before
Now that you've rephrased it that way the whole thing is obvious. If you have a very large sequence of numbers (representing a big natural number), it would be quite surprising if there weren't a three there. As most natural numbers are really big ones, we can conclude the initial statement.
Except it doesn't, with the same logic the probability of any given number to NOT contain a 3 would be 1-(1/10)^n which tends towards 1 when n tends towards infinity. So with this logic, each number as a probability of 1 to contain AND to not contain a 3 when n goes towards infinity. But i think the whole point is the video was posted on the 1st of april.
@@debbiescott8520 Actually your logic does not hold. The probability of a large number not containing a 3 would be (9/10)^n, as each digit has a 9/10 chance of not being a 3. What you found is the probability of a number not containing only 3s, which does tend towards 1.
While the nature of the video may have been that it's a silly sort of thing to prove, the mathematics of the proof are accurate.
this video is literally "hmmm yes this floor here is made out of floor..."
33like
🤣🤣🤣🤣
This was on April first
@@vinos1629 i am aware.
Basically, he having a trip
Not only is 3 everywhere, but brown paper is too.
+314rft I like James' reason.
"He just thinks it sounds funnier"
lelelelel
Such a toilet joke.
Brown paper is so much better than a chalk board because you can save all your equations and then use it to wallpaper your bedroom. A chalk board just gets wiped off by some unknown entity like Mom or cleaning staff and then you have to do it all over again.
1.1kth like !
The number 3 is everywhere, exept at Valve
Lol
CeeDee Player Don't be so mean to Lord Gaben, just because he didn't get the same education as us doesn't mean you have to mock him /s
***** /s /s /s loool this is just sarcasm amirite guys /s /s I know it's hard to tell /s so if you can't read I got these cool markers for you /s /s /s
/s
Gentelmen Z
and many did too, just look by yourself
CeeDee Player I saw...
Rated "T" for Three.
Only three year old can see this insane math equation
Its funny because I just learned about integers
@@anGelMaRtiNez-hw2bz I m proud of u :)
Ok no I’m going sleep tonight I don’t know what’s going on I’m
@MintyKPt morning my friend is doing a
Tree?
When he opened the calculator app, I felt that.
What..?
@@Sciencedoneright idk
d
@@Sciencedoneright Bruce is contained within the Cellular Telephone.
@@IrvingIVsame
All I thought while watching this video... "but this should work for every number"....
aaaand during the end of the video I´m like.... "aaaaaaah"
OPEN MIND same here lol
OPEN MIND Exactly hahaha
OPEN MIND Me too!
33 LIKES .-.
+OPEN MIND Same Here
Also 3 is everywhere except at Valve
bruhh XD
Lol, well played.
Headshot!!!!
Monokite Daiiiim
Monokite You stole this!
"He just thinks it sounds funnier"
I thought the number 3 had some special property or something...
Demyte D-1248 It’s funny because Valve can’t count to 3.
It’s funny because e = 3 = pi
@@purrplaysLE you mean e < 3 < π ?
@@SpiderMan-in9rl No. I think you probably don't know the Fundamental Theorem of Engineering. e = 3 = π. cos(x) = 1, sin(x) = 0.
@@VivekYadav-ds8oz lol
6:13 he asked exactly what I was thinking.
Yes, exactly what everyone is thinking
Same
3 is actually everywhere.
Except for one video game company in Bellevue, WA
explain?
@@leolaserbolt ima guess they are referring to half life
@The coo - king yeah I do know that half life is a game of it's own. I didn't know about people requesting portal 3 actually. I was just referring to the "half life 3 confirmed" meme that has been going around for quite some time
Funny valve jokes
Jokes on you they're making a three-quel
Sooooo everything is everywhere ?
Thats deep.
How do I pronounce your name?
as you see it
I'm ftom Slovakia
Shimon Kondrk ;)
Šimon Kondrk čus !
ahoj °-°
Took me exactly 2 minutes before realizing this was an April fools joke. Well played.
But all of the calculations are correct, it is indeed correct. That's just infinity in it's weirdness
The proof is propably mostly useless but not false
@@paulkonig9942 yes
It's not a joke. The proof is accurate, just useless as all 10 digits share that property, along with any finite combination of them (no idea about infinite combinations).
@@ADthehawk it both is and isn’t. An infinite string of 1’s is 100% included, but all the digits of Pi isn’t
This is a pretty exciting video for someone starting combinatorics... Otherwise it is pretty 1st of April video 😂😂
Hol up
I liked it
Yup. April fool... Hehehe
ohhhh it was April fools vid. That makes sense even tho it was still pretty legit.
1 and 4 are everywhere as well.
For instance, in the upload date of this video.
Seems intuitive. As the number of digits in your given number increases toward infinity, the probability that any specific numeral is left out approaches zero.
Precisely.
Almost all numbers have more than a sextillion digits.
2:12
Fun fact: those digits are the first 3 digits of e. (2.71)
Yeah, i thaught IT might approach e when i saw this😂
Impossible, e = 3
@@JohnSmith-kj2od Ah the engineer
@@jann4189 I was like, e. things approach e. I was so excited when he put down the 1 - (9/10)^n, which looked to me like (1 + 1/n)^n
This should’ve been posted on March 3rd 2013😂
Or march 3 3333
You're cute btw
it was posted on april 1st for a reason
@@NullTheCursed simp
March 3, 3 A. D.
Actually, it's because 3 means 3 sides which means a triangle which means ILLUMINATI and ILLUMINATI IS EVERYWHERE
Half life 3 confirmed.
333 likes. #illuminati
yaseen reza #iamilluminati:O
yaseen reza hahahahahhahhahha
Celebrating 420 '+1's
Throughout the entire video i was thinking to myself "But wouldn't this work for all single digit numbers" and i was getting more and more worried they weren't going to cover it and then at the end i let out a sigh of relief
the amount of comments taking this seriously and not realizing it's an april fools joke.. simultaneously painful and hilarious 😭😂
oh
well that makes a lot more sense then 😐
I learnt this in my math class, it's pretty much true. Probably posted on April 1st because it sounds so preposterous, but if you watch the video he shows the complete working out... It's funnier to see the people calling this a joke and not understanding the math /lh
@@lalat8920 it is a joke, because it is obvious but they treat it like it's something awesome and incredible in the video
He said 3 because it has a reputation of being mystical and having something to do with the mysteries of the universe.
"He just thinks it sounds funnier."
...You know what, it kinda does.
Especially when you consider that Valve can't count to three.
He just thinks it sounds funnier.
Valve and 3? HAHAHAHAHAHAHAHAHAHAHA i need friends
No, it doesn't compared to 0 (nut).
@@milopezusmc *press NUT button*
Meanwhile, at Valve...
This video could be also relationed to the biggest unsolved pi problem: if pi is a normal number that is if there is all numbers contained in the digits of pi in any base not just systems of base 10.
This was the best troll video I've seen in a long while. Thanks for making me laugh though!
In binary, all whole numbers contain the number 1 XD
Yeah, not just "almost" all but litterally all whole numbers (except 0) :P
hmm, what about 0 itself?
0 is a natural number though.
"grabs popcorn"
you can have 0 objects, yes.
Those are called positive integers. That´s a different category.
As a 999 addicted, I noticed something quite peculiar: the sum of all the digits (or digital root) of the numbers of 3 in each part always equals 1.
- 1 is self explanatory,
- 19 = 1+9 = 10 = 1+0 = 1
- 271 = 2+7+1 = 10 = 1+0 = 1
- 3439 = 3+4+3+9 = 19 = 1+9 = 10 = 1+0 = 1
A lot of old Numberphile videos have been popping into my recommended videos lately, and I'm so happy this gem was one if them.
Happy birthday to the channel! This was the first Numberphile video I ever watched and wanted to revisit it to celebrate the occasion
We should take number 3 and push it somewhere else!
Commented 3 years ago
@@tomekksiazek9007 HAH! Commented 3 days ago....it's actually pretty funny from my perspective.
@@afiffarhati4580 commented 33 minutes ago xD
@@tomekksiazek9007 *NOICE*
I really wished for someone to continue the comment chain , thanks....but now that it can't be continued anymore , guess i should break it myself......very sad :(
@@tomekksiazek9007 commented 3 months ago lol
So, almost all numbers contains almost all numbers...? 6:13
“Three o'clock. Three o'clock is always too late or too early for anything you want to do. An odd moment in the afternoon.”
― Jean-Paul Sartre, Nausea
But 3 is practically one of the last things you can reduce everything to, and 3 is almost found in everything...
This was uploaded on April fools...
+Pixelater4 Wow, you're right.
Today is April Fools. (When I posted this comment it was 2016)
>.>
Too bad the math still checks out
lol
I GOT IT! HL3 CONFIRMED!!!!!!
Congrats! Almost all your videos are amazing!
Me watching this: "Let's just check the date for april fools..." 😂😂
correct title: "almost all numbers contain any given digit"
infinity breaks maths. again.
Math is crazy due to fact that all numbers contain digits that are 0,1,2,3,4,5,6,7,8,9 at the same timem
Dr James Grime, the gift that keeps giving !!
Meaning the same for all other natural numbers. But then again, it would mean that 100% of numbers contain all the digits, 1-9.
HALF LIFE THREE CONFIRMED! :P
Before clicking, I said to my brother “you know, almost every number contains a 3”.
Not only is 3 in most numbers but it can also help with orders of magnitude & sometimes powers of ten
This video is produced by numberphile. Numberphile = Number + phile. Phile = file. You use a file for long nails. Nails are made of metal. Metal is cold. So is antarctica. Penguins live in antarctica. Penguins are birds. So are mockingjays. Monkingjays are in the hunger games. Hunger is when you don't have enough to eat. All animals eat. Humans are animals. Suspicious? Humans are born with 300 bones. There was a movie called 300. It was based off of a war. War backwards is raw. Raw meat makes you sick. You throw up when you get sick. Throwing up is called vomiting. Vomit starts with v. V is the 22nd letter in the alphabet. 22 is a number. So is 6. This video is over 6 minutes long. This video explains facts about the number 3. There are 3 sides on a triangle. Pyramids are made of triangles. Pyramids were built a long time ago. THE ILLUMINATI WAS FOUNDED A LONG TIME AGO. illuminati confirmed m8
+AirplaneDude It's around 300 bones. Your logic is flawed.
Yes Zarozapa CnJ
+airplanedude And nails aren't cold, they're just better conductors as they are made of iron, and so more quickly disperse the temperature of the nail with the approximately 20 degree warmer heat of your body giving the illusion of feeling a colder object because our perception of heat is flawed.
+airplanedude Phile means to love, so number lover.
+airplanedude When do we get to the ducks?
This was posted on April Fools but the math seems to check out
Indeed. The only prank is that it's attributed to 3. It's true of all digits in all number systems.
Did you watch the Video till the end? xD
SirSkyRage yea. guess I didn't get the joke when I first watched this
April fool's day is 4-1...which equals 3!
@@digitalfootballer9032 xD
Something about the date is just sketchy
April fools, that means 04.01.
4-1=3
Mind.
Blown.
Damn, I feel like a fool for actually trying to believe that 3 was different even though I knew it was not.
Damn it, I hoped 3 would be special in some way. I have OCD and all my checking and handle-touching compulsions are centered on the number 3, things have to be checked 3 times, touched in 3 places, etc. Also I get the urge to "make" right-facing right triangles with the 3 points.
Why 3 damn it?!
So,there are illuminati everywhere?
Hahhh hehe
是
6:13 The camera guy is the GOAT of this channel. He always asks the exact questions I’m thinking throughout these videos.
The short answer is P(number of n digits has no 3 in it) = (9/10)^n goes to 0 as n goes to inf.
Everywhere except in Gabe Newell's world.
Tricky The Clown IM THE 100TH LIKE
Tricky The Clown I WAS JUST ABOUT TO SAY THAT!
Tricky The Clown madness combat :D
Nathan Wood Dude, he said that 4 months ago... and I know you said this a week ago, but damn...
*****
That's what I thought.
Soooo almost all numbers contains all numbers? Deal with it!
gabriel passos actually, what Lorenzo Santi said is correct and more generalised. Because it would also be true that almost all numbers contain any digit sequence you can think of, not dist single digits.
I love Dr. Grimes All Videos...❤️
I love this channel.
At 1:15, he said "It's not point one," and I thought "Yes it is point one!". I later realized that he was using the word "not" to mean 0, lol.
+bun bacheso actually it's "nought", a British English variant of "zero".
Matthieu Houriet Oh, I see. Haha! Thanks. (I guess I should realize that, because in the USA, when we want to say that something is pointless, sometimes we say, "It's all for nought.")
It's his accent. He's from the North of England. See Game of Thrones for a point of reference :)
Holly, his accent is so cool!
Fun fact: Here in Brazil we say "porra nenhuma" when we want to refer to something that is equal (or even very close) to 0!
This works with strings of digits as well. Almost all numbers contain a string of a trillion consecutive threes.
I thought this sounded a bit ridiculous, but then I realised when you start getting into larger and larger numbers, each number has a lot of digits. When you start tallying up numbers with 100 digits, what's the chance there'll be _no_ 3's? Very low. So most numbers with, say, 100 digits, will contain at least one of each number between 0 and 9.
You guys are Awesome.
And what about Half-Life?
You stole my idea!
Niiiiiiiiiiko Nope.mp2 episode 2
+Bill Kerman Thumbs up.
Nope.mp4
What about Banjo Threeie?
all digits are everywhere duuh
Just like the number 23. I can see it everywhere.
This works only because numbers overlap, for example numbers with 3, and 7 under 100, 37, 73, then multiply by 10 to get anything in that set.
For anyone who doesn't get it basically this works because at every multiple of ten there is another digit in that number.
Although of course, this can be generalised for other bases. :-)
I guess you'd say: if b is our base (e.g. 10 for decimal, 16 for hexdecimal), then (b↑n - (b-1)↑n) ÷ (b↑n)) tends towards 1 no matter the value of b, so in hexadecimal, almost all numbers contain a 3 (albeit a different set of numbers to that in decimal), and almost all numbers contain any one of the hexadecimal digits.
Cool fact, IMO: in binary (base 2), *all* positive integers contain a 1, not just *almost* all, although as you might guess, the number 0 does not contain a 1. However, almost all numbers contain a significant 0, just as in decimal.
Also, the first significant figure of any non-zero integer in binary is always a 1, as there are no other options besides zero and leading zeroes are not significant figures. This is made use of in the storage of floating point (binary) numbers in computing, where the leading zero of any number is not stored, to save space for one extra significant figure (in the 'significand').
BTW, a lot of interesting facts about numbers in decimal apply just as well in other bases (although sometimes for different sets of numbers), and it's amazing how different things can look through the eyes of a different base. The Hardy-Ramanujan number, 1729, doesn't look special in any way, unless you see it written in duodecimal or dozenal (base 12), under which it is written as 1001, at which point it becomes obvious that it's equal to 12 cubed plus one.
3 is almost everywhere.
Triangles have 3 angle.
1776 is divisible by 3.
The British fought the Americans for 8 years during the revolution.
8 is 2 to the power of 3
Doritos have 3 angles
HALF LIFE 3 CONFIRMED!!!!
gg
gg
nice one hahahaha
+Christopher Halim ggwp
+Christopher Halim thank mr monstrata
I checked the date of this video. Glad I did. :)
Had a feeling during the middle of the video that it was uploaded on April 1st lol. Didn't even finish watching the full video.
If you write all numbers in binary, none of them contain the digit 3 :P
Hacks
+Sammy HAAAAAAAAAAAAX!
tru
11 does
+Константин Константин In trinary it's still true that no numbers contain the digit three!
on the first point, arent all numbers (0-9) in almost every number? not just 3? or am i just missing the point of the first segment.
this can be proven for every number.
look at this in binary notation and you get the point of the idea really easy :D
Watch it till the end, he says you can do it for other single digit integers
i was thinking the same thing
Jambott Do you not know what April fools is?
To put it in simple terms almost all numbers contain 3 as we tend to larger numbers but we can't get there, infinity is an amazing concept 🙏
This guy will most definitely be invited to my perfect dinner.
3 is everywhere except in the VALVe headquarters.
Looking at the comments, I see many people did this same joke 2 years ago.
I'm writing from the year 2018 to tell you there's still no HL3 in sight.
Apparently not Valve Games
OMG
As a limit problem, it shows the problem with limits, because it says eventually, all numbers contain 3.
Numberblock Three's favorite Numberphile video.
so you could so almost all numbers contain all the numbers :|
ILLUMINATI CONFIRMED
WhAt does that have to do with 3? Just wondering.
Downton 654 Triangle
+Zirg Gurj ohhhhhhh!
+Zirg Gurj I believe thou meanst to say "Half-Life 3 confirmed".
+E1craZ4life Portal 3 confirmed :p
3:59 it's 9 choices for first number because you can't use zero. Otherwise it will be 3-digits number. And you can have 00aa or 000a. It's not 4-digit numbers. It's 1-9999 numbers.
It literally means:
I can think of infinite numbers that contain a three.
I can think of infinite numbers that don't contain a three.
Therefore, there are equal amounts.
But the numbers that have a three are somehow more than the numbers that don't.
Just cannot escape '3'. It is in math and how many of one thing I see when drunk.
It's rising toward 100% because of the lenght of number, and the higher probability that any digit in that number is 3 (or any other digit). Awesome video :)
If you think about it, there are infinite number of integers while there's only Ten digits to choose from. Those digits will be used often as the integer goes up.
I just love this so much. It's funny, how stupidly right this statement is!
It makes sense, the bigger numbers get the more numerical digits they share. 123,456,789 contains all the numerical digits in one number. It would be very rare for extremely large numbers not to have every numerical digit in them, just as it would be rare to have a string of 100 digits and not have every number in it.
Qaedtg H you forgot 0
Acceleratus Just add a zero at the start
can't you just do this with every number?
Actually, just means that an infinite number contain every number ! Logic
Watch the end
Yeah, and this is awesome!! There are some many numbers between zero and infinity that 100 per cent have all numbers, maybe Descartes was right when said about infinity...
almost all numbers contain any prespecified sequence of m digits
Yeah, I think they went with 3 to grab our attention. You see, a lot of cultures have really strong, even mystical expectations for the number 3. It's my personal suspicion that this video was more of an exercise in playing with expectations, because, yes, obviously we can do this type of calculation for any single-digit number. :-D
I love this one.
This is the first Numberphile video I understood from start to finish...
The numbers mentioned in this video were: 1, 19, 271, and 3,439
The sum of the digits in each number equal 1. Example: 1 + 9 = 10; 1 + 0 = 1. Another example: 2 + 7 + 1 = 10; 1 + 0 = 1. One more example: 3 + 4 + 3 + 9 = 19; 1 + 9 = 10; 1 + 0 = 1.
What a coincidence xD
BuildMeASnowmanBiatch 3439/19=181, 1+8+1=10, 1+0=1
271*181=49051, 4+9+0+5+1=19, 1+9=10, 1+0=1
3439*271=931969, 9+3+1+9+6+9=37, 3+7=10, 1+0=1
BuildMeASnowmanBiatch
That’s interesting, why is it that way?
Alex Hilgenberg I have no idea lol
If it's a coincidence, then there's a 1 / 10^4 chance of it being that way so it's really strange.
BuildMeASnowmanBiatch All those numbers you listed have a remainder of 1 when dividing by 3.
In fact, if you continually sum the digits of any number (as you did) and get to a number
BuildMeASnowmanBiatch Obviously, Half-Life 3 confirmed.
The right man to speak about the significance of 3 would be Nikola Tesla
I was just thinking about that :)
1123aka Why?
endofscene
Because nikola tesla was obsessed with the numbers 3, 6 and 9. he believed that that those numbers were VERY important, nobody knows why though. if you don't know who nikola tesla is you are probably an american brainwashed by edison propganda :)
endofscene
Marko k if you don't know who nikola tesla is you are probably an american brainwashed by edison propganda :) is actually true, edison made up a huge amount of things during the "War of Currents"
I dont know why im laughing hysterically 🤣
It’s an asymptotic formula. There will always be numbers containing no threes, regardless of how few integers contain three in comparison to the total.
It’s joke
isn't this true with every single number?
It is.
Watch the end of the video.
MrSasyB Yeh but then the illuminati wouldn't be confirmed
Jack Matthews GET OUT
Took me a little while but I got it. Was confused at first but it makes perfect sense if you remember that numbers get longer as you go higher. Longer numbers, more chance for your digit. Especially towards infinity.
This video made much more sense to me after I noticed the upload date.
I click thumbs up on almost all numberphile videos!