ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12
9,165,313
Published 2014-01-09
More links & stuff in full description below ↓↓↓
EXTRA ARTICLE BY TONY: bit.ly/TonyResponse
The sum of all natural numbers (from 1 to infinity) produces an "astounding" result.
ANOTHER PROOF & EXTRA FOOTAGE: • Sum of Natural Numbers (second proof ...
MORE: • Why -1/12 is a gold nugget
NY Times article on this: nyti.ms/1iftqSv
Tony Padilla and Ed Copeland are physicists at the University of Nottingham.
They talk physics at our sixty symbols channel: youtube.com/sixtysymbols
Grandi's Series: 1-1+1-1.... • One minus one plus one minus one - Nu...
Read more about divergent series: en.wikipedia.org/wiki/Divergent_series
We also hear that Chapter XIII of Konrad Knopp's book, "Theory and Application of Infinite Sequences and Series", is very good if you can get your hands on it.
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All Comments (21)
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so guys lesson today is if someone offers to give you 1 dollar today 2 dollars tomorrow ect ect dont take the deal since he is obviously trying to steal you
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i always multiply both sides by zero. Seems to fix things up pretty well.
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My IQ increased by -1/12 after watching this
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Mathematics when YouTube removes the dislike button:
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After having watched this video for infinite times, I realized that my knowledge had increased by a -1/12 factor every time I watched it.
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A simple stack overflow bug. God will patch it in the next update.
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The analytic continuation of the Riemann Zeta function does indeed map -1 to -1/12, however this does not mean that the sum of all positive integers is -1/12. The whole point of analytic continuation is to extend the function to the domain where the original function is divergent, and after doing that u CANNOT say that the original function maps the analytically continued domain to all these extended points
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We were allowed to make an intuitive conclusion about 1-1+1-1…, but weren’t allowed to make a much more intuitive conclusion about 1+2+3…
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Top 10 pranks that went too far.
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Me before watching this video: liar Me after watching this video: cheater
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It seems like there's all kinds of tricks you can pull to get whatever result you want, once you throw rigor out the window. For example, he took the average of 1 + 1 - 1 + ... to get 1/2. You could also do this: 1 - 1 + 1 - 1 ... = (1 + 1 + 1 ...) + (-1 - 1 - 1 ...) = (1 + 1 + 1...) - (1 + 1 + 1...) = 0
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I think the biggest assumption is that S1 is 1/2 which I think is the reason why we got all the natural numbers sum to -1/12
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Let me prove that 1 = 0, using this premise: S1 = 1 + 2 + 3 + 4 + 5 ... = - 1/12 S1 - S1 = 1 + 2 + 3 + 4 + 5 + 6 ... - 1 - 2 - 3 - 4 - 5 ... = 1 + 1 + 1 + 1 + 1 + 1 ... Since S1 - S1 = - 1/12 - (- 1/12) = 0 It follows that 1 + 1 + 1 + 1 + 1 .... = 0 Let's name this sequence S2: S2 = 1 + 1 + 1 + 1 + 1 ... = 0 Now let's subtract it from itself: S2 - S2 = 1 + 1 + 1 + 1 + 1 ... - 1 - 1 - 1 - 1 .... = 1 Given that S2 equals 0, we can also write this as: 0 - 0 = 1 Which implies that 1 = 0.
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To quote a math teacher from my uni: "It's extremely unpleasant to approximate solutions that don't exist."
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Trolley Problem: A trolley is on a track headed towards one person, and after this one person is two people, and after that is 3 people, and so on. You can flip a lever to send the trolley onto an empty track. Do you flip the lever?
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The limit of the sequence of partial sums of the sequence is not 1/2. It does not exist. Stick to physics.
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Tony: "The answer can be either 1 or 0, so we take the average 1/2 Me: "Ok, now that's where you screwed up"
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This video represents negative knowledge; if you watch it, you will know less about mathematics than when you started.
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This is definitely mathematical hocus-pocus, as one of the primary postulates of mathematics is that the sum of two positive numbers is a positive number. That being true the sum of any number of positive numbers is also a positive number. That being true the sum of all positive numbers is also a positive number. I'm not sure what happened here that allows you to get this obviously incorrect answer oh, but it is obviously incorrect
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Mathematician: *calculates something, result doesn't make any sense.* Mathematician: "I define this as correct."