There's a strange number system, featured in the work of a dozen Fields Medalists, that helps solve problems that are intractable with real numbers. Head to https://brilliant.org/veritasium to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription.
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References:
Koblitz, N. (2012). p-adic Numbers, p-adic Analysis, and Zeta-Functions (Vol. 58). Springer Science & Business Media.
Amazing intro to p-adic numbers here: https://youtu.be/3gyHKCDq1YA
Excellent series on p-adic numbers: https://youtu.be/VTtBDSWR1Ac
Great videos by James Tanton: @JamesTantonMath
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Written by Derek Muller and Alex Kontorovich
Edited by Trenton Oliver
Animated by Mike Radjabov, Ivy Tello, Fabio Albertelli and Jakub Misiek
Filmed by Derek Muller
Additional video/photos supplied by Getty Images & Pond5
Music from Epidemic Sound & Jonny Hyman
Produced by Derek Muller, Petr Lebedev, & Emily Zhang
New 1: Taha’s Sequence
Rule: (Even ÷2) and (Odd × 2)
1- Find Set of Taha’s Sequence.
2- Find the loop of Taha’s Sequence.
New 2: Murad’s Sequence
Rule: (Even ÷ 2) and (Odd X 3) – 1
1- Find Set of Taha’s Sequence.
2- Find the loop of Murad’s Sequence.
@simonkristensson3077 Says:
I don’t quite get why mathematicians are so obsessed with this. So much rambling numbers, too little application in reality for my interest to spark.
It’s just a number with a particular property. But I guess I was lost confusion and missed the point😢
@NewAgeTorrez Says:
But if both equations are infinity to the left, then you'd never leave the first digit in the bottom. But how would this be useful to us, that arent mathematicians? I didnt finish the video. Made it 20:13. Nice videos! Educational & makes me use my brain again lol.
@NewAgeTorrez Says:
But if both equations are infinity to the left, then you'd never leave the first digit in the bottom.
@FireCamp105 Says:
I got a eureka moment remembering that if you just change it to base 2 and write the complement it's equivalent to writing a negative (we just stop somewhere becauses memory isn't infinite, and italways made sense to me but the same thing in base 10 seems confusing until the video starts distilling it bit by bit, and i started linking the 2 together and it clicked! Thank you for showing me something new
@Person-ef4xj Says:
Is it possible to also express irrational numbers like pi or sqrt(2) without digits to the right of the decimal place using the p-adic number system, and can imaginary numbers be expressed using p-adics?
@yohanlopes1847 Says:
it's very hard to find your videos by keywords of its contents, such as pattic numbers. Sometimes i remember of one to re-watch and just can't figure by the title they have on youtube 😢
@edelschrott Says:
17:19 it equals why not squared?
@ervivekchoubey Says:
..
@FearlessCuriosities Says:
after this video, i can confirm my insanity.
@SpartanFunnyProyect Says:
Hitler be like: 5:16
@billtraver1299 Says:
Love your math vids, I can’t find a definition for “ adic” as you said “10 adic” can you explain what adic refers to?
@bharanrajcrpf Says:
Sir please make a video on differential calculus
@dominicbonogofski Says:
20:36 Isn't -1/5 also an answer in this scenario, since multiplying 15 by -1/5 gives you -15/5, which equals -3, and adding 3 would therefore give you zero?
@himanshugarg6062 Says:
I've seen about 10-15 videos on p-adics on youtube but this is the only one that built an intuition for them by starting with a problem
@infuriated6243 Says:
when you say that in the p-adics that the only solution for multiplying to zero is if one of the numbers is infinite zeroes, why does ...20202020 and ...02020202 not work? can someone explain this to me
@artadray Says:
What a age we are living in? So much knowledge so easily accessible.
@emilvaldes3805 Says:
Isn’t…666666666667 = 2/3?
@sentientlvl.5mortar886 Says:
Is this similar to data/number overflow?
@user-lx2hb6wg6w Says:
as you add zero's there is a carry forward. what happens to that infinite 1
@alancornejo318 Says:
4:16 Hell no ...66666666667 = 2/3 ≠ 1/3
My whole elementary school was a lie
@alancornejo318 Says:
3:16 No no no 1/7 = 0,(142857143)
And this ...857142857143 is just a fragment of this number so the numbers after 8 are 241341758241....( I wrote these numbers in reverse)
@alancornejo318 Says:
4:40 Ok I no longer understand math
@viunetwork5142 Says:
5:27 Did anyone accept me ever think about that? E=-mc² (was Einstein wrong?)
@mossy_brickens Says:
My brain: that's actually interesting
Also my brain: hehe "why squared" hehe (0,0) looks like an owl
@Ankit655 Says:
Neither the title nor the thumbnail of the video indicates this is about p-adic numbers. It makes it hard to re-discover these videos. Please don't use clickbait-y titles.
@ponytreides Says:
pee addict
@randomrandomizer Says:
I need to watch this again. Lost me halfway.
@Effect_channel Says:
...9999999999+1=...11111111111110=10/9
@RitikMaurya07 Says:
2:37 this is actually similar to the decimal expansion of 1/7 just with a difference of the last digit which is 3.
@Veptis Says:
Are the animations running at a different framerate? It feels off
@potato9832 Says:
Fermat: Trust me, bro...
@Veptis Says:
x|5^2 is x*(x+1)|25 where | indicates concatination
@user-rn6wf3xh5o Says:
Around 4 minutes, you assert that .666666... x 3 = 1, but we all know that this = 2. 1/3 = .33333... right? I'm sure I'm not the first to notice this, but I'm surprised that this error has been left in after 10 months.
@user-pj5oe6rb4i Says:
what
my head hurts i forgot everything you said
@MimicMakesVideos Says:
I find it interesting that the 10-adic fractions look like… 1 - 1/n… with the ones digit rounded off
@Addy_The_Baddy Says:
so basically similar to binary arithmetic when handling negative numbers, with twos complement
@Noblesteed17 Says:
Fractal math
@cyndi5hunt Says:
This video enhanced my understanding of the two’s complement binary representation of negative numbers at a deeper level.
@rocketpower4127 Says:
What is infinity mod infinity
@8cto289 Says:
I just realized near the end that the reason the p-adics get smaller as they get longer probably has to do with how they are linked to decimals.
@yusefaltaher7288 Says:
Awesome
@adjoint_functor Says:
as a mathematician, i can confirm. i don't use numbers at all. that's for the machines and the machines only
/hj
@Icaruzin Says:
My brain ain't braining
@WKSOnce Says:
...999.999... = 0?
Is this the real world or just a fantasy;
Is a system with both p-adic and reals an escape from reality?
@GRE_GMAT_SAT Says:
Oh, thank you Sir.
This is what I worked on in my master dissertation.
@JurijFlugge Says:
at 4:51 we multiplay 99999... by 10 so at the end of it there should be a zero not a nine. so the total isnt nine but a bit less because we need to take somthing of the next number, that will repeat untill the end and total to 8.99999[...]9991
@xqandstuff Says:
this video infuriates me and interests me at the same time
@AhmedHassan-xy4iv Says:
I’m man enough to switch off at 20 minutes.. brainy hurty
@ACuriousChild Says:
0 does NOT EXIST in REALITY - I just realised that while watching the video. It has been "invented" by the mind in order to pretend that REALITY - GOD ALMIGHTY - can be mathematically proven. Which is just not the case. Does it mean the convention 0 is NOT TRUE - YES and NO.
1. In REALITY - NO
2. In THE MATERIAL - YES as it serves the purpose to solve equations applying to THE MATERIAL but NOT TO THE WHOLE encompassing GOD ALMIGHTY - like the "negative" being the basis of a photo. THE MATERIAL being the photo, while the negative remains hidden "behind the curtain".
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