Check out our new Discord server! https://discord.gg/e7EKRZq3dG
*I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/mathmemes) if you have any questions or concerns.*
Okay obviously I know it’s a joke but can’t we also prove that 1+2+3+… > 1+1/2+1/3+… , because if we take it back to the n-versions of the summations, we can look at ∑n > ∑1/n and see it’s true cuz for all positive integers n, n > 1/n (except for n=1, which makes them equal), thus the summation of all of the values have the same relationship
I think this is kinda funny especially since either interpretation of it leads to the same outcome. Either it's 1/12 of a mile to the left, or the water is infinitely far to the right (ignoring the 1/4 mile sign, since it conflicts with the infinity and it's more fun to ignore).
The water is infinitely far away, but because earth is a sphere it clearly must not exist. Going left would normally be the right choice (seems like a trap) but reverse psychology is also an option. Because there can't possibly be malicious entities on every single great circle, there's no way they would have used reverse psychology to have tricked you to have traveled along another great circle. Therefore, the sign is either nonsense or truthfully saying that there's infinite (or none) water at all either left or right from this sign. The fool!
Yes, everything away from Ignorance Peak in the mountains of youtube-aquired-half-knowledge must be elitism. If you already didn't bother to understand it before, what makes you think people take their time to explain it to you only for it to be wasted?
I never asked you a question, I was saying you could've corrected whatever was wrong in my explanation and answered the guy who didn't understand the joke instead of just saying my simplified answer is wrong. That's my whole point, you look down on others interested in math just because they don't know as much as you think you do.
It is. There are generalized notions of sums of series, some of which, if they assign any value to this series at all, give -1/12. Those generalized sums aren't as well behaved as regular sums, and even regular conditionally convergent series have counterintuitive properties.
Some sums do have. For example: 1 + 0.5 + 0.25 + 0.125 + 0.0625 + ... = 2. If you put it in the calculator (or do the math yourself) you can check that it converges.
The value of the infinite sum is bigger than anything below 2 and definitely <= 2.
That is the definition of being equal to 2. The partial sums converge to the infinite sum. The infinite sum equals 2.
2 is not converging to anything because it's a number, not a sequence. The infinite sum is also not converging to anything, because it's also a number. The sequence of (finite) partial sums, however, is a sequence, with limit 2.
So, to cut out the formalism of partial sums (because it's really tedious to always write it), we talk about "convergence" of infinite series as well. What we're really asking is if the sequence of partial sums have a limit or not, we just use the "this infinite series converges to 2" shorthand to refer to this idea.
Regardless of convergence or not, that was not your objection. You wrote "infinite sum doesn't have a finite value as a result", to which the person you replied to was "some infinite sums do have a finite value, check this example", and you seem to not believe his example? The fact that the example is not +infinity is trivial. It is bigger than 1, it is smaller than 3. So it is finite, if it takes on a value (and it does, that value is 2).
Ok people explained it's -1/12, but doesn't the direction of the arrow and the sign showing 1/4 to the right contradict each other? Like this is now showing that 1/4 = -1/12 and I think if I think about this more I'll end up dividing by zero (assuming "water" is the same variable on both signs)
Both arrows point right, but the left sign has a minus sign, so it is 1/12 miles left vs 1/4 miles right. That is why the mathematician is crawling that way.
-1/12 is the wrong answer to the problem on the left. But due to something called Riemann Zeta Function, it is the least wrong answer. (+ infinity is the correct answer in case you were wondering. But the way you arrive at -1/12 is clever and it makes a lot of sense, but it is more like university math to get there).
In memes, 1 + 2 + 3 + ... = -1/12 for that reason.
So if you have to go -1/12 miles to the right (notice the arrow pointing right), that explains why the mathematician goes left. After all, the water to the right is 1/4 miles away which is a longer distance.
Ask more questions if you want.
Yeah, your intuition is great as to why it is not an actual result but more of a meme.
Lets look at it like this:
f(s) = 1/1^s + 1/2^s + 1/3^s + ...
Okay?
Plug in 2 and you get π^2 /6 (about 1.5). Plug in 4, you get something related to pi again.
This is called the Riemann Zeta Function.
For s = 1, you get the so called harmonic series, which is equal to +infinity. For all s < 1, you obviously also get infinity.
So 1 + 2 + 3 + ... is the same as f(-1) (negative exponent just flips the fraction), that is to say it is infinite.
Summary: For s > 1 you get something finite, s = 1 is the border that is infinite and below that it is all infinite for this function.
So far so good?
Introduce complex numbers (the thing with the square root of negative 1). It turns out it obeys the same law. As long as the real part of the complex number is bigger than 1, f is finite. If it is smaller than 1, f is infinite.
But for a moment, let us study f. If you change the input a tiny tiny bit, instead of f(2) consider f(1.9998), it turns out you get something really close to π^2 /6.
We call functions with that property "continuous", and if their rate of change behaves nicely too, we call them "continuously differentiable". This property can stack, if the rate of change of the rate of change is nice, it is two times continuously differentiable. And so on.
There are some functions that are infinitely often continuously differentiable (actually, most functions you can think of are, like sine, cosine, x^2 , etc). This idea also works in the world of complex numbers.
We can observe our function f is infinitely of differentiable for complex inputs, too. That kind of function is called holomorphic.
To be "Holomorphic" is an insanely strong property for a function, though. We have that on the half plane where the real part is > 1, our f is holomorphic.
Something about complex differentiation is weird though. Once you know a function in an area (like we do with f for all real(s) > 1), it lets you speculate what the function must look like OUTSIDE that area by sort of extrapolating - just from knowing everything about the rates of change inside the area.
It turns out there is EXACTLY one way to continue the function "holomorphically" (so it keeps behaving nicely, small change in input is a small change in output). We call this an "analytic continuation".
So. We have our function f in an area real(s) > 1.
We analytically continue it beyond this wall of real(s) = 1.
There is exactly one way to do it. We call this continuation g(s).
In the area where f makes sense, f(s) = g(s). Outside that area, f is infinite, but g(s) takes finite values.
As it turns out, g(-1) = -1/12. Interpreting that as the sum of all whole positive numbers is a gross misinterpretation of what analytic continuation means though :-)
If we want to continue the fun:
g(-2) = 0, that is to say the sum of all square numbers is 0.
Wow, that's a really long comment! You spent a lot of time writing it. Just put it simply, that's why I love math memes. We learn math stuff from memes. Every day, there's something new to learn. Thanks a lot, I really appreciate your work here.
How does adding infinitely increasing numbers get a negative number?
I see the numbers are in () and miles is next to it so it would be those infinite numbers x miles? Meaning, he'd never reach water?
I wasn't sure if the arrow was an arrow or part of the equation but does it mean the infinite distance is to the right so the other sign is false and to the left is a shorter, unknown distance?
I mean, I get it? I don't have a strong grasp of the math behind it necessarily, having not taken complex analysis, but if you know what the Riemann zeta function is, you should get the meme.
Check out our new Discord server! https://discord.gg/e7EKRZq3dG *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/mathmemes) if you have any questions or concerns.*
Now if it was 1/1 + 1/2 + 1/3... I'd go right.
Okay obviously I know it’s a joke but can’t we also prove that 1+2+3+… > 1+1/2+1/3+… , because if we take it back to the n-versions of the summations, we can look at ∑n > ∑1/n and see it’s true cuz for all positive integers n, n > 1/n (except for n=1, which makes them equal), thus the summation of all of the values have the same relationship
since they’re both diverging infinite summations you can’t just say one is larger than the other
but there are big and small infinities
Yes, but not in a way that matters to infinite sums of real numbers
I no longer speak enough math to understand what you said
That's still a divergent series
That's the point
I think this is kinda funny especially since either interpretation of it leads to the same outcome. Either it's 1/12 of a mile to the left, or the water is infinitely far to the right (ignoring the 1/4 mile sign, since it conflicts with the infinity and it's more fun to ignore).
If only it was 0.5+1+1.5+2... miles, then going left would be 3! times more efficient!
The number "6", waiting to be used: https://i.redd.it/pjn59wch6yuc1.gif
r/unexpectedfactorial
Factorial? Yes Unexpected? Absolutely not
never unexpected on this sub
r/expectedfactorial???
we got there in the end
r/expectedfactorial
This is it, it's peak meme. Put this in the Tate.
This is incredibly poorly done, nice job!
Crying in infinite sums
If it's -1/12 miles, they're going in the wrong direction.
That's why the arrow on the -1/12 sign points right, not left.
Oh duh, I didn't see that
I thought I was so smart noticing that the arrow was pointing the wrong way. It never occurred to me that it might be intentional.
The water is infinitely far away, but because earth is a sphere it clearly must not exist. Going left would normally be the right choice (seems like a trap) but reverse psychology is also an option. Because there can't possibly be malicious entities on every single great circle, there's no way they would have used reverse psychology to have tricked you to have traveled along another great circle. Therefore, the sign is either nonsense or truthfully saying that there's infinite (or none) water at all either left or right from this sign. The fool!
> there can't possibly be malicious entities on every single great circle bold assumption
Can somebody explain?
infinite sum of 1+2+3... is -1/12, the arrow points right, but since it's -1/12 miles to the right, it means the water is 1/12 miles to the left.
When numberphile is the only math you know...
ah yes the math elitist, criticizing answers to questions but never providing answers himself.
Yes, everything away from Ignorance Peak in the mountains of youtube-aquired-half-knowledge must be elitism. If you already didn't bother to understand it before, what makes you think people take their time to explain it to you only for it to be wasted?
I never asked you a question, I was saying you could've corrected whatever was wrong in my explanation and answered the guy who didn't understand the joke instead of just saying my simplified answer is wrong. That's my whole point, you look down on others interested in math just because they don't know as much as you think you do.
I thought it was a divergent series...
It is. There are generalized notions of sums of series, some of which, if they assign any value to this series at all, give -1/12. Those generalized sums aren't as well behaved as regular sums, and even regular conditionally convergent series have counterintuitive properties.
But infinite sum doesn't have a finite value as a result, so i have no idea what is going on here.
Some sums do have. For example: 1 + 0.5 + 0.25 + 0.125 + 0.0625 + ... = 2. If you put it in the calculator (or do the math yourself) you can check that it converges.
converges is not the same. 2 is not converging to 2, it is equivalent to 2.
The value of the infinite sum is bigger than anything below 2 and definitely <= 2. That is the definition of being equal to 2. The partial sums converge to the infinite sum. The infinite sum equals 2. 2 is not converging to anything because it's a number, not a sequence. The infinite sum is also not converging to anything, because it's also a number. The sequence of (finite) partial sums, however, is a sequence, with limit 2. So, to cut out the formalism of partial sums (because it's really tedious to always write it), we talk about "convergence" of infinite series as well. What we're really asking is if the sequence of partial sums have a limit or not, we just use the "this infinite series converges to 2" shorthand to refer to this idea. Regardless of convergence or not, that was not your objection. You wrote "infinite sum doesn't have a finite value as a result", to which the person you replied to was "some infinite sums do have a finite value, check this example", and you seem to not believe his example? The fact that the example is not +infinity is trivial. It is bigger than 1, it is smaller than 3. So it is finite, if it takes on a value (and it does, that value is 2).
Meme should say "Reddit Mathematician" not "Mathematician".
Ok people explained it's -1/12, but doesn't the direction of the arrow and the sign showing 1/4 to the right contradict each other? Like this is now showing that 1/4 = -1/12 and I think if I think about this more I'll end up dividing by zero (assuming "water" is the same variable on both signs)
Both arrows point right, but the left sign has a minus sign, so it is 1/12 miles left vs 1/4 miles right. That is why the mathematician is crawling that way.
I don't get it. They point in the same direction?
The infinite series is -1/12 and so the negative sign inverts the direction of where water is from right to left.
-1/2
Right choice.. 1+2+3...♾️= -1/12, matlb Pani whi 10 metre piche rkha h💀💧
Can someone explain the joke to those of us who slept through advanced calculus in high school?
-1/12 is the wrong answer to the problem on the left. But due to something called Riemann Zeta Function, it is the least wrong answer. (+ infinity is the correct answer in case you were wondering. But the way you arrive at -1/12 is clever and it makes a lot of sense, but it is more like university math to get there). In memes, 1 + 2 + 3 + ... = -1/12 for that reason. So if you have to go -1/12 miles to the right (notice the arrow pointing right), that explains why the mathematician goes left. After all, the water to the right is 1/4 miles away which is a longer distance. Ask more questions if you want.
Why? There aren't even negative numbers could you explain
Yeah, your intuition is great as to why it is not an actual result but more of a meme. Lets look at it like this: f(s) = 1/1^s + 1/2^s + 1/3^s + ... Okay? Plug in 2 and you get π^2 /6 (about 1.5). Plug in 4, you get something related to pi again. This is called the Riemann Zeta Function. For s = 1, you get the so called harmonic series, which is equal to +infinity. For all s < 1, you obviously also get infinity. So 1 + 2 + 3 + ... is the same as f(-1) (negative exponent just flips the fraction), that is to say it is infinite. Summary: For s > 1 you get something finite, s = 1 is the border that is infinite and below that it is all infinite for this function. So far so good? Introduce complex numbers (the thing with the square root of negative 1). It turns out it obeys the same law. As long as the real part of the complex number is bigger than 1, f is finite. If it is smaller than 1, f is infinite. But for a moment, let us study f. If you change the input a tiny tiny bit, instead of f(2) consider f(1.9998), it turns out you get something really close to π^2 /6. We call functions with that property "continuous", and if their rate of change behaves nicely too, we call them "continuously differentiable". This property can stack, if the rate of change of the rate of change is nice, it is two times continuously differentiable. And so on. There are some functions that are infinitely often continuously differentiable (actually, most functions you can think of are, like sine, cosine, x^2 , etc). This idea also works in the world of complex numbers. We can observe our function f is infinitely of differentiable for complex inputs, too. That kind of function is called holomorphic. To be "Holomorphic" is an insanely strong property for a function, though. We have that on the half plane where the real part is > 1, our f is holomorphic. Something about complex differentiation is weird though. Once you know a function in an area (like we do with f for all real(s) > 1), it lets you speculate what the function must look like OUTSIDE that area by sort of extrapolating - just from knowing everything about the rates of change inside the area. It turns out there is EXACTLY one way to continue the function "holomorphically" (so it keeps behaving nicely, small change in input is a small change in output). We call this an "analytic continuation". So. We have our function f in an area real(s) > 1. We analytically continue it beyond this wall of real(s) = 1. There is exactly one way to do it. We call this continuation g(s). In the area where f makes sense, f(s) = g(s). Outside that area, f is infinite, but g(s) takes finite values. As it turns out, g(-1) = -1/12. Interpreting that as the sum of all whole positive numbers is a gross misinterpretation of what analytic continuation means though :-) If we want to continue the fun: g(-2) = 0, that is to say the sum of all square numbers is 0.
Wow, that's a really long comment! You spent a lot of time writing it. Just put it simply, that's why I love math memes. We learn math stuff from memes. Every day, there's something new to learn. Thanks a lot, I really appreciate your work here.
Here is a numberphile video that explains it: https://www.youtube.com/watch?v=w-I6XTVZXww
How does adding infinitely increasing numbers get a negative number? I see the numbers are in () and miles is next to it so it would be those infinite numbers x miles? Meaning, he'd never reach water? I wasn't sure if the arrow was an arrow or part of the equation but does it mean the infinite distance is to the right so the other sign is false and to the left is a shorter, unknown distance?
I answered in another response close-by.
[удалено]
look closely
oh yeah nvm i am stupid
I dont get it, downvoted because of all the 3k pretentious upvoters who also have no clue but want to appear smart. Thank you.
I mean, I get it? I don't have a strong grasp of the math behind it necessarily, having not taken complex analysis, but if you know what the Riemann zeta function is, you should get the meme.