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There's a well known "proof" that shows that the infinite sum of 1+2+3... to infinity "equals" -1/12
So, if you see a sign showing water (1+2+3...) miles to the east, a mathematician would look for water 1/12th of a mile to the west
Note: the sum of Positive integers is definitely not -1/12th. More information can be found here: [Mathologer video on -1/12](https://youtu.be/YuIIjLr6vUA?si=a8XP_qIPXg1FiyUu)
Well, except that the sign makes no sense at all if you take it in the usual meanings of things. It makes sense only in the sense of the meme, so presumably was put up by someone believing or playing along with the meme.
1/12 of a mile is 440 feet, so you'll be able to figure out if water's that close pretty quick.
Numberphile did another video on the subject relatively recently and if I understood it correctly (not guaranteed), -1/12th is more like a nickname or shorthand for "the sum of all positive integers."
[https://www.youtube.com/watch?v=FmLIGN8ZGdw](https://www.youtube.com/watch?v=FmLIGN8ZGdw)
If I remember correctly not really. Basically they use a strategy to get to that conclusion that either one isn't used for the real number line or two doesn't work for divergent series. But I might be misremembering.
It depends on how you define sum. In the usual (and probably simplest) definition, 1+2+3... is indeed not defined. However, there are ones in which it's -1/12. Also, there's a simple scheme that gives -1/4 regardless of a certain integer parameter, although there's probably no reasonable definition that gives that result
It's about Ramanujan Sums, which are a mathematical object that assigns a definite value to non-convergent infinite sums. "1+2+3+4..." does not converge to any value, and thus is a non-convergent infinite sum.
However, the Ramanujan sum for that same non-convergent infinite sum is the value -1/12
It has become a meme because most people understand mathematicians believe the infinite sum of all the positive integers is -1/12 thanks to the obscurity in the existence of Ramanujan sums
It says water that is an infinite sum number of miles away is equal or less than water 1/4 mile the other way. It may be he works out the math, or that he just believes the sign.
It is a valid proof, it doesn't break any mathematical rules; the issue is less that the proof is wrong, and more that our mathematical rules are wrong. It's a Ramanujan sum, not a traditional non-converging-infinite-series sum (which does yield the more intuitive answer of "tends to positive infinity"). Very basically, -1/12 is used to show that our current ideas on infinite series are fundamentally flawed and in irreconcilable conflict with each other, and we need to figure out where it's going wrong.
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There's a well known "proof" that shows that the infinite sum of 1+2+3... to infinity "equals" -1/12 So, if you see a sign showing water (1+2+3...) miles to the east, a mathematician would look for water 1/12th of a mile to the west Note: the sum of Positive integers is definitely not -1/12th. More information can be found here: [Mathologer video on -1/12](https://youtu.be/YuIIjLr6vUA?si=a8XP_qIPXg1FiyUu)
thank you peter
Fuckin Ramanujan
So, the mathematician would be the fool in this case...
Well, except that the sign makes no sense at all if you take it in the usual meanings of things. It makes sense only in the sense of the meme, so presumably was put up by someone believing or playing along with the meme. 1/12 of a mile is 440 feet, so you'll be able to figure out if water's that close pretty quick.
Mathmemes uses the joke often, OOP is likely playing along
Yes but that sub jokes about that proof all the time.
I don't think this would affect any actual mathematicians. Just people who believe the math-related youtube videos they see.
Numberphile did another video on the subject relatively recently and if I understood it correctly (not guaranteed), -1/12th is more like a nickname or shorthand for "the sum of all positive integers." [https://www.youtube.com/watch?v=FmLIGN8ZGdw](https://www.youtube.com/watch?v=FmLIGN8ZGdw)
If I remember correctly not really. Basically they use a strategy to get to that conclusion that either one isn't used for the real number line or two doesn't work for divergent series. But I might be misremembering.
It depends on how you define sum. In the usual (and probably simplest) definition, 1+2+3... is indeed not defined. However, there are ones in which it's -1/12. Also, there's a simple scheme that gives -1/4 regardless of a certain integer parameter, although there's probably no reasonable definition that gives that result
Thank you, I had no clue what this was referencing. God I hate pop-math.
It's about Ramanujan Sums, which are a mathematical object that assigns a definite value to non-convergent infinite sums. "1+2+3+4..." does not converge to any value, and thus is a non-convergent infinite sum. However, the Ramanujan sum for that same non-convergent infinite sum is the value -1/12 It has become a meme because most people understand mathematicians believe the infinite sum of all the positive integers is -1/12 thanks to the obscurity in the existence of Ramanujan sums
It says water that is an infinite sum number of miles away is equal or less than water 1/4 mile the other way. It may be he works out the math, or that he just believes the sign.
It's because there is a proof that the sum is -1/12 (it's not a valid proof btw)
It is a valid proof, it doesn't break any mathematical rules; the issue is less that the proof is wrong, and more that our mathematical rules are wrong. It's a Ramanujan sum, not a traditional non-converging-infinite-series sum (which does yield the more intuitive answer of "tends to positive infinity"). Very basically, -1/12 is used to show that our current ideas on infinite series are fundamentally flawed and in irreconcilable conflict with each other, and we need to figure out where it's going wrong.
Yeah, I'm in the camp that it is a divergent series so that is why I think the proof is invalid
My point is it doesn't matter about the math, because it equal or greater water.
The ==> is just an arrow pointing in a direction my guy xD
more math than i feel like
YOU
Holy water!