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From: numberphile
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  • Dear algebra; Please stop asking me to find your x. She's gone. She's moved on.

  • 496 likes, perfect number

  • Funny, I paused this video to go do something, and I ended up pausing it at 0:16 without trying.

  • "Lets get rid of the kids and replace them with tasty drinks" XD

  • Do they have a video for every number?

  • I don't think she knows what a perfect square is...

  • I just realized that, in theory, if we take the limit as x -> infinity, and as y-> infinity, then x^y = y^x as well, but since infinity is only a concept and isn't recognized as a number, i'm sure that's why they didn't consider this in the video.16 reigns supreme!

  • THAT is NOT an X

  • 16 is also a base 2 for bianary 1 2 4 8 16 32 64 128 256 512 1024 2046 4096
  • Triangle numbers please :D

  • "Why don't we get rid of the schoolkids and just replace them with tasty beverages?"

  • damn these mathematicians ,im barely passing geometry

  • lol 1 will almost work for this, but x and y will already equal themselves. also im pretty sure that the reason 16 works for this is because 4 is the only number that's square can also be added to itself to equal 4. 2 x 2 = 4, and 2 + 2 = 4

  • It's maths

  • Well.... Shorthand version: nothing else can be x^y=y^x when x =/= y because the equation will only work if y is a power of x or vice versa, due to the fact that if the numbers are not powers of each other they will have different prime factorizations, and thus be different numbers. If you go even one number higher like 3^9 vs. 9^3, it becomes clear that the high value of the exponent of x overrides the high value of y.

  • Ah man, smart and beautiful.

  • 4 and 2... 42. The answer to everything... XD

  • 02:46

    No you don't put it into a calculator, you do it in your head since the numbers are so low.

    And you should look into complex x and y, that would be way more fascinating.

  • It's not really a property of 16, it's a property of 4 and 2 being so low. That's also what allows the small numbers to be prime (2,3,5,7).

  • 16 is my favourite number- born on 16th of march and sometimes (not as much now) it just pops out at me... like often if Im walking down a road, the first and only house number I glance at is 16 haha

  • I was born on 16 December too ;D

  • IT"S MATH, DAMMIT! SINGULAR!

  • I found a function that is very close to the graph visualised by x^y=y^x

    It is (y-(e-sqrt(e))(x-(e-sqrt(e))=e

    Don't ask me why it is :p

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  • Dr Ria Symonds looks like she gives an enthusiastic blowjob

  • "can I order to the table 4 squared?", lol what a jackass..:D

  • I hate the way she draw the x !

  • a^b = b^a where a≠b

    the only solutions are 2 & 4, 4 & -0.766665696, 2 & -0.766665696.

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  • I find very things in this universe so supremely beautiful as a pretty girl with a thing for mathematics. Hot like lava.

  • Maths Jams sound awesome. I occasionally meet up & play maths with some of my friends, it's good. But where is the proof that this relation work for any other intergers?

  • why is it on the seecond last tuesday??

  • I was born on 16 December too!!!! :P

  • I'm born on August 16th =D

  • Porn for us (nerds)

  • Are there any complex numbers satisfying x^y = y^x?

  • "We accidentially did maths". Somehow, that's just an awesome quote.

  • Taking x or y=1 is trivial, and won't work. For x=2, we have y=4 gives us 16, 3 doesn't work and anything larger will give 2^y=/=y^2, because the LHS will be bigger.

    In general, for x bigger than 2 (x<y), it's going to be the case that x^y is much larger than y^x (this is quite obvious, taking larger powers has a larger effect than taking smaller powers of larger numbers, but not enough room here to show this rigorously, but it's easy).

  • she draws her x's like a buttcrack lol I'd learn math from her <3

  • She makes gross 6's

  • hat about "1" and "0"!!?!?!?!

  • @MrNoookie It may seem illogical, but for every x, x^0=1.

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  • Has anyone found the proof for x^y=y^x? I tried looking or it and the only thing I found was on some sight called Ask Doctor Math but the explanation was only partial and confusing.

  • @elizze6 I can disprove it right now.

    x = 3

    y = 2

    3^2 = 9

    2^3 = 8

    9 does NOT equal 3, therefore x^y = y^x is not true for the set of all real numbers.

  • @belliebum12 change the 3 to an 8

  • @belliebum12 I know it doesn't work for all real numbers. I'm just wondering why it ONLY works for x=4 and y=2.

  • In response to being asked to serve food to table 2 to the power 4: Sorry sir we don't serve arses here.

  • Do the British also have Sciences Jams?

  • Was this filmed in London St Pancras train station?

  • zzzzzzzzzzzzzzzzzzz

  • 0:07 ... he sounded like such a paedophile xD Sweet 16!!! :L my favourite age :D .. I mean number....

  • The dangers of being too clever when dealing with waiting staff...now I want a Peroni...

  • Wow, she's CUTE!

  • Ohhh she has a loop in her hair... So sweet <3

  • Do a video on the number 108. That number follows me everywhere!!

  • @Luigi4911 is that your IQ?

  • @teknown Is that supposed to be a joke? Because it is an average IQ so it wouldn't really be a good joke then.

  • @LamaPaj it wasn't a joke, just a funny coincidence ^^

  • Still wonder why they choose 42 as the answer to all and every thing.

  • what a coincidence, my penis measures 16 inches

  • That waitress spat in your food.

  • If anyone is still looking for a simple proof for this x^y = x^y -> x^y = 16 "problem" given in the video and can't find something on the internet just like I couldn't (mainly because you don't really know what to search for), I came up with one and wrote it down:

    gammahoo[.]de/sixteen (remove the brackets)

  • You must do a video about the golden ration or 1,6180...

  • @superfunny1972 I think they're only doing integer numbers for now but I don't know for sure. Besides there already is a video on the golden ratio by sixtysymbols which is another channel by Brady so I wouldn't expect that too soon. :P

  • 23 Enigma, please look into it. The single most frequent number I notice in my life everyday.

  • why not remove the school kids and replace them with tasty beverages? lol

  • throughout the whole time he was talking i was thinking..that guys gonna tip his beer over.

  • My favorite number is 16 because that's when MOTHERFUCKING CHARMANDER evolves to MOTHERFUCKING CHARMELEON

  • @andrew14566 You have 16 thumbs up!

  • @andrew14566 FUCK YEAH!!!!!

  • @andrew14566 Thats freaking wierd only a few hours ago was the first time i heard about charmander and turning into charmelon!

  • @KDDIRL Never tried a charmelon. Is that like a charmango?

  • @iantheuncountable Actually it's even better: that property of 4 holds for every hyperoperation not just the ones you mentioned. :P

  • 16 ounces of beer gone to waste.

  • i like this number because i like 16 y.o. girls.

  • i would bang her

  • The beer dude! THE BEER!!!!!

  • is that british Jason Segel?

  • What if X and Y are not integers?

  • @BeastOfTraal plot x^y=y^x with wolfram alpha.

  • I'd say 4 is an even cooler number than 16. 2 + 2 = 2 * 2 = 2^2 = 4, and what's more, each of those expressions that equal 4 has exactly 2 operands.

  • What does pub guy do for a living now that he's no longer teaching?

  • That beer is still full...

  • 2 and 4 are not the only numbers that the X and Y can represent to get 16. You ever think of 16 to the 1st? I swear, I'm sick of these people who flunked out of Math and Physics 101 trying to do YouTube videos.

  • @FastFoodConnoisseur "you ever think of 16 to the 1st". Hm, so according to you 16^1 = 1^16 -> 16 = 1

    Lol, are you retarded or just stupid? Besides "these people who flunked out of Math and Physics 101" are mostly maths or physics professors.

  • Brady, I am sorry to say that so far, this is the least interesting channel. It seems rather arbitrary in the way videos are done so far. I think more complicated mathematics would be more interesting: Fermat's Last Theorem, or perhaps some complicated mathematical problems; issues in the field.

  • @4jonah

    Check out claymath (dot) org and look at the Millennium problems. They are supposedly the most difficult unsolved math problems. I don't even understand the explanations given, so perhaps some videos on those?

  • Can you show me how to divide matricies?

  • @DionysianUrge Multiply by the (Pseudo-) Inverse.

  • @GammahooX I didn't think it was possible... I have been shown the light!

  • Can somebody please post a proof?

  • Great video! Do you only do integer videos, or would you do a video on say Liouville's number?

  • these video's are cool, but i can usually only handel 2 minutes of them

  • do number 69 or 64 plz

  • Can you have a look a 32 please?

    I'm an Engineering student a Nottingham and love your videos especially the one with the Tetris champion

    However 32 I think is interesting. Apparently is you ask someone to pick a number between 50 and 1, them not being allowed to pick 50, or 1, 32 is the most picked number.

    It was only when I heard this and thought about it that I realised how often when posed with picking a random number that I picked 32. Since hearing this I've now seen how often it occurs

  • I'm an (ICT) teacher. I totally agree with the idea of getting rid of the kids and replacing them with a tasty drink ;-)

  • @numberphile would that not be cubed instead of square

  • This channel should give out problems like these and then give the answer (if there is one) in a following episode ^^

  • this channel is getting boring already

  • 22 is a pretty cool number... Can you do a video about it?

  • ok... I've been playing with this since I've seen it, besides 16, is it possible to find the same thing for rational numbers

    where x != y are rational and x^y=y^x

    anyone tried it?

  • Her smile is beautiful.

  • @Requiemes I was thinking the same... ;)

  • or do the number 64 please

  • do 69..

  • so is 81 

  • miss walaces ass is so fine

  • im kidin i be trollin

  • no one wants to hear ur life story u fukin retard

  • Do a video on what happens when you divide a number above 0 by 0! :D

  • @Dribblehand I always found the limit as x approaches 0 of x/x more interesting.

  • @Mewigi What's interesting about that? x/x the x's cancel, the limit is 1, problem solved.

  • @GammahooX Wait shit, you're right. I meant just 0/0, not a limit. I was tired.

  • @Dribblehand That will be the number itself ;-)

    :factorial:

  • @Dribblehand infinite, if using limits

  • @Dribblehand no number can be divided by 0 (even 0 cant be devided by itself), they could make a video about why you cant do that, but its kind of simple: divide 12 apples on 2 piles -> you 6 on each pile. divde 12 apples on 0 piles -> there are no piles, but where are the apples then? they have to be somewhere but the expression 12/0 gives them no space to be in. therefore x/0 is not defined (which is means the same as "you cant do that")

  • @Creepyseven You can define (and it makes sense in many cases) x/0 where x > 0 to be lim y->0 x/y in which case 12/0 would be infinity. 0/0 is a bit more interesting - it turns out that it often ends up being a hole in a function at a non-infinite point. For example the function (x-1)/(x^2-1) returns 0/0 at x=1 yet the graph would show that it should be 0.5 (and L'Hopitals Rule for that matter).

  • @Creepyseven I meant lim y->0+ x/y. Otherwise you will end up with +- infinity problems. :P

  • @Dribblehand Well if you have an n natural number, and you divide by 0!, you get n since 0! = 1

  • These guys seem to be even bigger nerds than the ones on the other channels - love it!!!

  • She is BEAUTIFUL!!!

    She could talk math to me anytime

    <3

  • A example? What else is a perfect square

  • @GSA14101996 the doc meant in terms of the other perfect thingies, like 3^3, 4^4, etc... some shoddy editing probably didn't help.

  • @GSA14101996 Yeah that was a brain malfunction :-) If the base had to be the same as the exponent then 2 ^ 2 would be the only perfect square. Perfect squares have integer / whole number roots, so 9 is a perfect square because the root is a round 3. Square any of the integers 1,2,3,4,5,6,... and you will arrive at a perfect square. All numbers greater than zero have a real square root, but only the perfect squares have integer roots.

  • @darkdudironaji If I understood the video right the first number in the binary sequence was 0 and the last was 255. If that is true then the 8-bit processor holds 256 numbers - 1 thru 255 plus the additional digit 0. One of the few circumstances when a number plus 0 equals another number!

  • Look at the web address it says: Uploademail

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  • This kind of video suits my mathematical maturity level perfectly :)

  • "why we dont we get ride of the school kids and replace them with tastey beverages" lol

  • I am so going to the next mathjam in Glasgow !!!

  • @m1t3com PS: I would be very nice to make videos with more advanced maths

  • Squares are orderly, rational, and mostly a man-made geometrical idea - they're extremely rare in nature aren't they? Why then are they so useful to mankind? It would be interesting to talk about others: triangles, circles, hexagons, pentagons, etc. and the individual properties associated with each.

  • my favourite # is phi. even though I was born on April 4. (04 * 04 = 16) woa! so much co-incedienceerbly

  • happly waiting for the 36 vid now :D

  • It says this video was posted 16 hours ago. hmm :)

  • 16 squares is a much better presentation than the unit circle.

  • It is like asking for another number that when multiplied by itself or raised to the power of itself is equal to the same number, just 2 and 1 can do that. Because for these two numbers it is the same operation. Needless to say, 2^2=2*2=4 so 2^4=4^2.

  • 16 is also the square root of your last video, 256: although you claim it is about the number 255 incorrectly!

  • @singlespies agreed, because 255 is the 256th positive integer d^_^b

    I'm also disappointed that they did a video on 16 and did not mention the hexadecimal number system.

    And speaking of roots, powers and squares of the 16 and 255/256 videos: In adition to 16^2 = 256, the root of 16 (4) by the power of itself (x^x) is 256, which makes 256 the perfect square of a perfect square :D

    All of these numbers are fun, since they are all in the line 2 in powers of 2 in powers of 2...

  • @gulllars we're doing a different video on hexidecimal...

  • @gulllars 255 is the 255th positive integer. 0 isn't positive or negative.

  • @singlespies No, they're correct. An 8 bit processor can only go up to 255. The easiest way to tell is the windows calculator. Make the view "programmer" and put in 255. Then click the bubble next to "bin" it will give you the binary, which is 11111111. If you do the same thing for 256 you would get 100000000. 256 in binary is 9 numbers long, so it wont fit in an 8 bit processor.

  • @darkdudironaji this is a number about 16 not 255

  • i feel like u guess never have working markers

  • I once asked if I could have some food and booze delivered to table 4 squared.

    The bartender punched me in the throat and called me a prick.

  • Did you do a video on the square root of -1 yet?

    Or was that just my imagination?

  • @culwin lol

    but srsly, they really should do a video on it...

  • so some bar wench didnt understand that 4 squared is 16 yet she has no problem charging a ridiculous price for a cold beer??!!

  • XD get rid of the schoolkids and replace them with tasty beverages xD

  • I 3 16

  • great video, but i don't know what this world is coming to if we need a calculator for 2^4. just sayin' xD

  • Do a video on 1337

  • Interesting.

  • Do a vid on 100

  • do a video on 0!!

  • Can you guys do anything with 1's?

  • My birthday's feb 1st

  • The x^y=y^x problem is actually doable for anyone who knows basic differential calculus, and it's fun to solve.

  • @wesselbindt You can do it without calculus too I believe...

  • Too bad this wasn't posted on the 20th because I just turned 16 on the 20th.

  • my personal opinion - good video, but too long for something simple. Something like this should be done in a minute - like MinutePhysics :)

    well done :)

  • @Geeoorrgeee You must of missed the part where they were talking about other things. If someone wanted to only find out why 16 is so great, they could of googled it. These videos offer interaction, their stories -and- the subject matter.

  • @QwoPhasaArius thank you for kind of getting the other dimension of these videos... though perhaps your average numberphile is less interested in such things! ;)

  • thats not how u write an x

  • These videos are great!

  • @Villex93 thank you!

  • 0.0625 also satisfies this.

    ((-2)^(-4)) Equals ((-4)^(-2)); y equals-2; x equals-4. this satisfies x^y equals y^x because its 0.0625 so its not the only number that is a square of a perfect square.