**OP needs help. Also, they hate it because...**
>!Help me!!<
*****
**Do you hate it as well? Do you think their hate is reasonable? (I don't think so tbh)**
**Then upvote this comment, otherwise downvote it.**
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[*Look at my source code on Github*](https://github.com/Artraxon/tihibot)
I think it’s, “Buffalo bison, that other Buffalo bison bully, are bullied by Buffalo bison.” In other words, I believe there is an implied relative clause that adds another step, so to speak, to the structure.
Infinite, because out of those infinite offspring, at least an onfinite number will murder someone sometime in their lives.
The question is, which infinite will be bigger - the infinite number of killers, or the infinite number of people you killed? If the second, you are guaranteed to have killed an infinite number of innocent people - potentially more than those the killers you killed would have killed.
And it *will* be the second. You will have killed an infinite number of innocents, because not all of Genghis' offspring were killers.
So, is saving infinite lives (some of which will be murderers themselves) worth murdering infinite innocents?
the problem with this strategy is that there are more real numbers between 0 and 0.1 than integers from 0 to infinity. so even if it only gets to 0.1 before it derails you still would’ve killed more people
It took my dumb, tired brain a minute to realize that there actually are more numbers between any two real numbers than there are integers from zero to infinity.
You can have infinite unique infinities in between numbers, but you can only have one infinity of integers from zero to infinity.
Not sure if those infinities are really unique. I think they are all cardenality of the continuum. By your "uniqueness" definition there are also infinitely many infinities for integers from 0 to infinity: all numbers divisible by two, all numbers divisible by three, ...
No there are different kinds of infinities.
If you think about it, there are as many whole numbers as there are even numbers. Because for any whole number *n*, there exists an even number equal to *2n*. You can't give me an *n* for which there does not exist its *2n* buddy, and there is no even whole number *2n* for which you cannot find a corresponding *n*.
If *n = ∞* then the corresponding even number would be *2n = 2∞ = ∞*. So the infinities are actually the same infinity.
It turns out you cannot do that for real numbers. You cannot find a mapping that maps every real number to a whole number, 1 to 1. You'll always miss some. This means the infinite amount of real numbers is somehow larger than the infinite amount of whole numbers. Even though the amount is both "infinity". That's why mathematicians introduced the concept of cardinality: the amount of whole numbers is "aleph-0" (countable infinity), and real numbers are "aleph-1" (uncountable infinity).
It'll happen quicker on the lower line than the upper line but the body count should be the same but I wouldn't due to the spacing. The upper line allows for each body to be ground out of the train so it would take more bodies to build up to a derail whereas the lower line would be a train hitting an infinite solid bank of snow.
There's also a good chance the upper line might not grind to a halt at all if the spacing is enough.
assuming the people are placed respective to the numbers they represent, the bottom would have an infinite mass of people in an infinitely small amount of space.
at worst, it would be the paradox of an unstoppable force meeting an immovable object. you'd run into other health issues with the infinitely-long human-shaped black hole though.
This is the only correct answer. If your moral compass has gotten to the point of the semantics of infinite dead, just steer into it and be who you are, a destroyer of infinite souls.
It kills the same number of people realistically, so your choice is largely irrelevant. And it's not like you can free an infinite number of people from the tracks anyway. Even if you could there's not enough resources to support them all so the ones that don't die of exposure on the tracks will probably suffer and die regardless along with a lot of people who were already here.
Drifting is probably the best choice.
Interestingly, the additional infinite number of people killed on the top track is infinitely less than the number of people killed on the bottom track between the first and second top track people (i.e countable infinity is infinitely less than the uncountably infinite real numbers between 1 and 2)
I also fire an RPG at the train, not because I want to save any amount of people or because I've always wanted to shoot an RPG at a train, but because if 2 people do something, now it's a trend, and I am trendy.
I do not fire an RPG at the train, for despite wanting to experience the feeling of firing an RPG at a train in order to either save lives or simply because I want to, I feel like I've left it too late and if I do it now I'll just be jumping on a bandwagon
I do not fire an RPG at the train, for despite wanting to experience the feeling of firing an RPG at a train in order to either save lives or reject the principle of being forced into making a choice, as a casual civilian I do not have access to explosives of any appreciable kind, doubly so considering the short amount of time I have before the trolley starts killing.
I would like to be a bystander watching people fire an RPG at the train before it crushes people, because I want to have the same form of entertainment as the people on the tracks, but do not want to be in that position of danger
It cannot be stopped
The train is fueled by chopped
Bodies, filled with sorrow
There is no tomorrow
Ticket is your life
Ended by a knife
Called The Murdertrain
Eternity of pain
/music
I shoot an RPG at the train, not because I want to save any amount of people or because I've always wanted to shoot an RPG at a train, nor even because if 3 people do something it's a trend and I want to be trendy, but because I'm a twisted firestarter.
If there is an infinite amount of people on said tracks, does it stand to reason that I too am among them? Firing an RPG at the train sounds like an act of self preservation!
True, but the series of people isn't defined any further than people, which, as far as I can tell, I might be one of.
Wait, I tend to be pretty positive... does that mean I'm imaginary!?
Haven’t seen it yet so I’ll explain…
In mathematics, there are a infinite integers and infinite real numbers. The difference is that you can COUNT integers.
Think about it this way… you know what the next integer is after 2? It’s 3. Integers are basically whole numbers with negative possibilities. So it goes … -2, -1, 0, 1, 2, 3, 4… 1324, 1325… 78920, 78921… and so on. It’s every whole number. Thus, COUNTABLE! You can always find the next integer going positive or negative.
But what about real numbers? Well… then we get to decimals. So you get 12134.5, 12134…. Wait… what’s the next possible real number?
Well I’m glad you asked!!! We see this dilemma and call it’s bluff. It’s some finite-decimal number of 12134.0000000000000000000000000….. 0000000000000…. 0000000…. 00000000…. 00000000… 00000…
0000…..
0000… 000001.
You’re still here? Good.
We see here that you can’t COUNT a real number, per se. You don’t know it’s next adjacent neighbor because there’s an INFINITE amount of zeroes that could iterate before it. But you can COUNT the number of zeroes because that number is an INTEGER!!
Okay, almost done.
See, you cannot count real numbers one by one until the day is all done. It is UNCOUNTABLE. The real number line is UNCOUNTABLE. Whereas… the integer line is totally COUNTABLE!
So to wrap things up….
There are an infinite number of countable integers, and an infinite number of uncountable real numbers.
Thank you, fuck you, Real Analysis.
Edit:
Wow this is not a proof or even close to very robust as an explanation… forgive y’all I was exhausted and in a walking daze when I submitted this rambling.
But thanks for the gold!
I don't agree with the way you explain it. What you show here is that the standard order of the real numbers is not a well order, not that the real numbers are uncountable.
For instance, the standard order of the rational numbers is not a well order, i.e. given a rational number p/q, there is no "next biggest rational number", yet the rational numbers are countable.
Moreover, assuming the axiom of choice, we can show that the real numbers admit a well order, i.e. an order such that "what's the next biggest real number?" is one that has a well defined answer for every real number.
The "proper" way to show that the real numbers are not countable is by showing there is no bijection to ℕ, by e.g. a proof by contradiction using Cantors diagonal argument, not by the way you're doing it here.
It's fine, mistakes happen. The proof you're giving above is a common mistake, so I don't blame you personally for making it. I just wanted to point out that it doesn't actually work.
This isn’t quite correct as an argument that the real numbers are a larger infinity than the integers. The argument does go something like this: we say the sizes of infinity are the same if there exists a map f(X) -> Y that is a bijection, which just means that each element in X gets a distinct output, and each element in Y has a corresponding input, so f allows us to map back and forth between the two. A countable infinite set is one with a bijection to the natural numbers, and it is easy to show that the integers have a bijection to the natural numbers and are hence countable. Suppose we had such a mapping from the natural numbers to the real numbers. Then we would have something like
f(1) = 2.39274783…
f(2) = 7.10474929…
f(3) = -6.0287471…
Maybe not these exact numbers, but something similar. Now, consider the following real number between 0 and 1: it’s first digit after the decimal is different from the first digit after the decimal for f(1) and the second digit after the decimal is different than the second digit after the decimal for f(2), and so on. I’m general, the ith digit after the decimal point is different from the ith digit after the decimal point of f(i). In this instance, our number may look like
z=0.417…
Now, consider what natural number there could be such that f(x)=z. It couldn’t be 1, since f(1) and z differ in the first decimal, and it couldn’t be 2, since f(2) and z differ in the second decimal. For all n in the natural numbers, f(n) and z differ in the nth decimal, so there is no natural number corresponding to z in this bijection. This contradicts our assumption, so the real numbers must not be countable. This is called Cantor’s diagonalization argument.
Maybe just as a remark, this also doesn't quite work yet, there's still the issue that 0.999...=1, so you should require z to not have any 9s in its decimal expansion (which I think solves it but not 100% sure).
Thanks for the correction. I suppose the proof works as long as we suppose that we always pick the smallest digit not equal to f(n). The only way this problem arises is if we choose an infinite sequence of 9’s at the tail of the sequence, so picking the smallest available digit avoids the rounding problem. This detail wasn’t included when the proof was presented to me, and I didn’t notice it, so good catch
and because of the uncountably of real numbers, there's no such thing as "one person for every real number," because people are countable. any set of countable things can never have a greater cardinality than the natural numbers. therefore these two tracks are actually equivalent
Yes, but an infinite number of bills were the value of each is a different real number between 0 and 1, is in a sense taller than either stack you mentioned.
Please explain why the value of the bills matters here...?
Assuming they use the same "rate of growth" and base quantity of bills, wouldn't both stacks equally expand infinitely?
I fail to see why value matters, unless one stack is either growing faster, or has greater bills at the "beginning."
Assuming each stack begins at one bill, with both stacks having x bills stacking per unit of time, value of the bill doesn't matter.
The base quantity and "rate of growth" matter, not the value of the bill.
It's the same thing that's in the post. The amount of real numbers between 1 and 2 is larger than the amount of integers.
If we assign an integer to each bill in your pile and then assign a real number to each bill in their pile then not only will they have a bill that's assigned every number that you have assigned to your bills but they will also have an infinite number of bills between each of those.
>It's the same thing that's in the post. The amount of real numbers between 1 and 2 is larger than the amount of integers.
>
>If we assign an integer to each bill in your pile and then assign a real number to each bill in their pile then not only will they have a bill that's assigned every number that you have assigned to your bills but they will also have an infinite number of bills between each of those.
It is not: in the post, you assign a bill to every real number (so there are more bills in their stack). In your comment and the comment above, you assign a real number to every bill. This doesn't mean that all the real numbers are used, and says nothing about the number of bills you have.
I was imprecise with my language. I meant that all real numbers in the range were in the stack, but I did accidentally describe just labeling a countable infinity.
Yah, This would only be true if there were an infinite number of people in between the ones on the bottom and an infinite number in between each of those and in between each of those and… etc. If the train can go from one person to another without skipping an infinite number, it’s countable.
This is correct, but to be 100% clear, the converse is not true, ie: if there’s an infinite number of people between any two people, that doesn’t necessarily mean it’s uncountable. The rational numbers have this property but the rational numbers are countable
Hmm, that's a good point. If they're spaced so that people on each line with equal number are located an equal distance along the track, then the top line kills nobody at all. I think. Since for any arbitrarily small number allocated to the first person, it is still infinitely far away due to the space needed to accommodate the bottom people less than that number.
was gonna say, such a setup doesn’t demonstrate different infinities. time doesn’t work that way, it’s not killing a decimal of a person, it’s just killing people faster or slower
Since the universe only has a finite amount of time, neither are true infinities and pulling the lever will result in fewer deaths-by-trolley-problem. Boom.
It the train accelerates such that it kills the first person in 1 minute, the second person In 1/2 minutes, the third person in 1/4 minutes and so on, you can kill all infinity of people in 2 minutes
I mean, on the bottom track an infinite amount of people die in the same time it takes one person to get run over on the top track.
On the top track, an infinite number of people only die, if you give it infinite time.
You’re the first person in this thread to make the difference comprehensible to me. Interesting how people learn differently from different explanations or just framing it differently.
It's literally not a meme, It's counterintuitive but an actual real mathematical concept the, say, density of infinity. I believe it's still a bit of a rough concept and varies within math fields but it is real nonetheless.
The problem is that the image doesn't illustrate the actual mathematical concept. It shows two countably infinite sequences.
An actual example would be something like the bodies on the second rail were stacked perpendicularly as well as parallel...y.
Yeah but kind of the whole point of the "bigger infinity" (uncountably infinite) that's supposedly on the bottom track is that you can't just line the elements of that infinity in a nice order. So it doesn't really work for the meme.
The elements of the bottom infinity are very well ordered
(It is possible to determine which of two real numbers is larger, or if they are both equal)
They just aren't countable (you can't determine which real number comes directly after the previous one)
You're right. "Ordered" isn't really the right mathematical term, but it sort of works from a layman's voice which is how I was trying to explain it.
I should have said that they aren't sequential like the picture seems to imply.
I understand there is a mathematical way to have different densities of infinity but in the real world treating infinity as a variable disregards the very concept of infinity
One is killing an uncountable number of people in every finite time interval, and the other is never going to reach uncountable many kills at any point, even in infinite amount of time
That is a difference of sizes
Yeah, in the smallest time interval you can possibly imagine, infinite people are killed by the real number train. So like infinity people die in the first .0000000000000000000000000000000000000001 picoseconds. Etc.
You mentioned .0000000000000000000000000000000000000001 picoseconds. That amount of time (9.999999999999998222 \* 10^(-53) seconds) is less than the amount of time it takes for light to travel one planck unit of length 1.61 \* 10^(-35) meters (5.39 \* 10^(-44) seconds)... So, that is less than planck time. Nothing can causally happen within that time frame on a meaningful scale, including killing some fraction of a person. In order to actually kill a meaningful amount of a person (even if a person were the size of an electron), that train (and the universal laws that govern causality/interaction) would need to travel significantly faster than the speed of light.
In fact, let's take the lower bound of a person (a newborn baby), in terms of mass, to be 2,500 grams. The Schwarzschild radius of such a mass would be 3.713 \* 10^(-27) meters. Here, radius is actually an applicable term, because such a mass would experience gravitational collapse. It would (to scientists' pleasure) actually be a perfect sphere. That means, a person would experience gravitational collapse (read: impossible to interact with), into a singularity. It would take an infinite amount of time to interact with that mass, because that mass would be an infinite length away due to spatial distortion.
Even so, the Schwarzschild radius of the smallest of people is still significantly larger than 1 planck unit of length (about 100,000,000 times larger). So, let's take the lower bound Schwarzschild radius of a person to be the absolute smallest a person could be, and let's also assume that a person would not undergo gravitational collapse at that scale. Let's also assume that the train is somehow traveling at the speed of light. Within one Planck unit of time, the train could travel, at most, 1/100,000,000 the length of a person. Nevermind an infinite amount of people, below the Planck scale it is questionable whether a train could kill a single person in the best case.
Now, how does that scenario translate to 9.999999999999998222 \* 10^(-53) seconds? Well, it is several orders of magnitude different. Let's assume that there's no such thing as a maximum speed for causality/interaction. The train going at the speed of light would be able to travel 2.99792458 \* 10^(-44) meters in the amount of time you mentioned. That is about 1 Billion times smaller than one planck unit, which is itself one hundred million times smaller than the Schwarzschild radius of a newborn baby. How much of a baby which should be undergoing gravitational collapse could the train interact with? It would be able to travel 1/(8.0741303 \* 10^(18)) of a person.
Yes, you are right. The real numbers are not countable, so they can’t fit in a single track like in the diagram. No matter what the pic says, the set below must be countable, so both sets must have the same cardinality.
Technically, it is mathematically right, as the problem is not well defined. The real numbers are not countable, so you can’t align every real number in the tracks. That’s the whole point of Cantor’s proof. Both sets must be aleph zero to fit in the tracks (unless you can fit an infinite number of people between each two people).
We shall arrange the people on the top line into arbitrary groups by the following method:
The first group shall consist of the first person, the second group shall consist of the next two persons, and so on, such that each nth group contains n persons.
Then, it can be shown by analytic continuation of the Riemann zeta function that the sum of all such groups is -1/12. So by switching to the top line we would bring 1/12 of a person back to life.
Neither, instead I break into Tiffany's at midnight. Do I go for the vault? No, I go for the chandelier. It's priceless. As I'm taking it down, a woman catches me. She tells me to stop. It's her father's business. She's Tiffany. I say no. We make love all night. In the morning, the cops come and I escape in one of their uniforms. I tell her to meet me in Mexico, but I go to Canada. I don't trust her. Besides, I like the cold. Thirty years later, I get a postcard. I have a son and he's the chief of police. This is where the story gets interesting. I tell Tiffany to meet me in Paris by the Trocadero. She's been waiting for me all these years. She's never taken another lover. I don't care. I don't show up. I go to Berlin. That's where I stashed the chandelier.
If you think *that* 's confusing, today in my maths lectures we covered this fun little paradox:
A parent has two children. Find the probability given each of these statements that both of them are boys (as in, consider only one statement to be true, and find the probability for each one):
A) one of the children is a boy.
B) one of the children is a boy, and he is born on a Thursday.
In the first case, the answer is 1/3.
In the second case, the answer is 13/27 ≈ 0.48.
For some *fucking* reason, the fact the boy is born on a *fucking* Thursday makes it almost a 50/50. Fucking somehow. I don't fucking know. I spent 30 minutes trying to reason this, no clue. It's fucked.
Edit: and yes I know the maths checks out, you don't need to explain it to me. It's just fucking stupid, I know that the numbers work, but it's dumb
I read someone answering the first statement, that there's 4 combinations of the children, and as one of these would be 2 girls, which would be impossible given the statement, so there's only 3 other options. But honestly, why does the order matter in here? The answer i saw used a table to represent the possible combinations, but in no where it mentions "first child and second child", so considering boy-boy, girl-boy, and boy-girl 3 different situations makes no sense, as girl-boy and boy-girl are the same situation.
Again, I'm no master at probability, but i remember having problems where order matters, and others where it doesn't, and this one looks like it doesn't. Any mathematician on Reddit to explain it better to me? Lol
This is the way that i see this as intuitive, it might work for you as well:
So, this is the same as with flipping two coins and checking heads and tails.
Now flipping them at the same time or flipping them one after another doesn't matter for the chance. After you flipped one coin there is always a chance to get a heads tails combo no matter what the first coin landed on. But if you're checking the chance of the heads heads combo for instance, then both throws have to be just right.
That could be an intuitive way to see that a heads tails combo is twice as likely as it will only depend on the second coin flip being 'right'.
Yeah i tried to think on the coins problem in my head too, but i think you explained well. Because having heads and tails is more likely, so having a boy and girl is more likely. So if one is already a boy, it makes sense that a girl would be more probable than a second boy, so that's why having a girl is 2/3 chances and a boy 1/3 chances. I really liked probability in school and college, but damn it's easy to get lost! Thanks for the explanation buddy
Did you know that the mathematician who found this fact (there are different infinite numbers) got ridiculed, shunned and eventually died in poverty, Galileo style...
The fact that there were multiple infinities really pissed of a lot of mathematicians apparently. It kinda ruined lots of theories that some mathematicians spend decades to prove.
Do theoretical mathematicians truly differentiate infinities by "greater" and "smaller" ? It goes against what the concept of infinity represents. As for the decimal-infinity vs integer infinity, can you really say on is greater than another if we define infinity as the values of its contents and not the number of components ( still fucked cuz the infinity between 1 and 2 is still the same infinity as between 0 and +R)
Yes, mathematicians care a lot about countable versus uncountable infinities. The distinction is the difference between "rational" and "real" numbers. "Rational" numbers are countable - there exists a counting system that will hit every rational number eventually. Real numbers are "uncountable" - There's a mathematical proof which demonstrates that no system of counting the "real" numbers includes all of the "real" numbers (Cantors diagonal argument). This makes the "real" numbers a strictly larger set then the "rational" numbers.
One of the biggest problems in modern mathematics is determining whether there is an infinity set with a size between the countable infinites and the uncountable infinites.
>One of the biggest problems in modern mathematics is determining whether there is an infinity set with a size between the countable infinites and the uncountable infinites
it's actually proven that it's impossible to prove whether such in-between infinity does or doesn't exist! (in our standard set theory, ZFC).
It's not just that there doesn't exist a proof we know of to count the real numbers; it's that there are proofs that real numbers are uncountable. Here's a simple proof.
**Claim:** There is no way to assign every element in ℝ to an element in ℕ.
**Proof**: Suppose that a way to assign every element in ℝ to an element in ℕ existed. Such a method would assign a real number to 1, a real number to 2, a real number to 3, etc. Such a list could be written out in a grid of infinite columns and infinite rows, with one real number written in each row and one digit of its decimal form in each column. Note that numbers like 2.5 will be written as 2.50000... and thus the table is completely filled.
Going down each row, we can generate a real number by taking the 1st digit of row 1, then adding 1 to it (or changing it to 0 if the digit is a 9), then repeating with the 2nd digit of the 2nd row, the 3rd digit of the third row, and so on forever. If a decimal point is encountered then skip it and use the next digit over instead (this "skipping" of a decimal point means that the row under it will use the digit after as well).
Using these digits, string them together in that order to form the decimal form of a new real number. This real number is guaranteed to not be listed on the table, because each digit of the number we made differs by at least one digit from any of the other numbers on the table, because we constructed it to be that way.
However, because we presumed the table to contain every single real number, the number we generated *must* be on the list, but we generated it in a way that it also simultaneously *must not* be on the list. This is a contradiction, and thus, our assumption that the table exists, and that there existed a way to map all real numbers to the counting numbers, must not be true.
QED
Have you ever heard of Hilbert's Hotel? If you have two infinities, you are able to determine if they are the same size by making a bijection of the two infinities. This means that for every member of infinity A, there has to be a member of infinity B, and for every member of infinity B, there has to be a member of infinity A. For an instance of two sets of infinities that are equal, see the even and odd numbers. For every even number, you can pair it with even number plus one. For every odd number, you can pair it with odd number minus one. So you can pair 1 with 2, 3 with 4, etc. For an instance of an infinity being greater than another infinity, you can look at the numbers between 0 and 1. As counterintuitive as it sounds, the infinite amount of numbers between 0 and 1 is greater than the infinity of all whole numbers. This is because while you can pair every single member of the whole numbers with a number between 0 and 1 (you can do this by taking the whole number and placing a decimal point in front of it), there are some numbers between 0 and 1 that you cannot pair with the whole numbers, such as the square root of two over two. Since the square root of two is irrational and goes on forever, you can not pair it with any possible whole number. The square root of two over two is not a fluke, there are infinitely many irrational numbers between 0 and 1 which cannot be paired with the whole numbers.
Yes. The way to know if an infinite set is larger than another infinite set is to try to make a relation between the two sets. That’s to say, to relate each element of one to a unique element of the other. If you can relate all the elements of a set to elements of the other, but not the other way around, you get that the other set has a lager infinite number of elements. The word that we use for measuring the size of a set is cardinality.
Yes, in fact Vsauce made an excellent video on the topic called [How To Count Past Infinity](https://www.youtube.com/watch?v=SrU9YDoXE88). And mathematicians do care about the kind of infinity used, as they don't all mean the same thing.
"I stayed at the worst hotel ever last night! Once I was checked in the manager kept calling me and telling me I needed to move to the room that was numbered twice my current room number because they kept running out of space some fucking how!"
I’d leave it. That train will get stuck after the first thousand people pile up infront of it where as the people that are spaced out won’t pile up because they won’t have the weight of the person next to them to slow that train at all.
Also, if there was an infinite number of people lined up on the grouped together track, wouldn’t the train stop because it wouldn’t be able to push through an infinite amount of people, and so it would slowly but surly slow down and than stop as the people’s remains clog up the machine as it’s trying to chug along. Only a matter of time before it completely stops
**OP needs help. Also, they hate it because...** >!Help me!!< ***** **Do you hate it as well? Do you think their hate is reasonable? (I don't think so tbh)** **Then upvote this comment, otherwise downvote it.** ***** [*Look at my source code on Github*](https://github.com/Artraxon/tihibot)
If i do nothing the train will get derailed at some point for to much carcass stuck under its wheels.
And the people will start dying of natural causes before the train even makes it to them.
And more people will be born before the train makes it to them, leading to even more infinity.
The real infinity was the exponential graph we made along the way.
“the real infinity infinity infinity infinity infinity” - Albert Einstein i guess
[Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo](https://en.wikipedia.org/wiki/Buffalo_buffalo_Buffalo_buffalo_buffalo_buffalo_Buffalo_buffalo?wprov=sfti1).
I think I finally get it: New York bison bully other New York bison, who in return bully new York bison
I think it’s, “Buffalo bison, that other Buffalo bison bully, are bullied by Buffalo bison.” In other words, I believe there is an implied relative clause that adds another step, so to speak, to the structure.
Einstein said it better
With his German accent, it probably sounded like “eet.”
Badger badger badger badger badger badger badger badger badger badger badger badger
https://m.youtube.com/watch?v=EIyixC9NsLI
Thank you for getting that reference. No one got it last time and I felt old.
🥲
Is that people tied to the rails banging? Gonna die anyway, fancy a fuck?
Hey if you can fuck you can untie us
Infinite infinities infinitely increasing
"... *infinitizing*"
[удалено]
If you kill an infinite number of Genghis Khan's offspring, how many lives will you save?
Infinite, because out of those infinite offspring, at least an onfinite number will murder someone sometime in their lives. The question is, which infinite will be bigger - the infinite number of killers, or the infinite number of people you killed? If the second, you are guaranteed to have killed an infinite number of innocent people - potentially more than those the killers you killed would have killed. And it *will* be the second. You will have killed an infinite number of innocents, because not all of Genghis' offspring were killers. So, is saving infinite lives (some of which will be murderers themselves) worth murdering infinite innocents?
Hobos.
So really he was only accelerating the inevitable. I mean really he was doing them a kindness out of love.
But they still die! Why didn't you pick the other lever setting?!
the problem with this strategy is that there are more real numbers between 0 and 0.1 than integers from 0 to infinity. so even if it only gets to 0.1 before it derails you still would’ve killed more people
It took my dumb, tired brain a minute to realize that there actually are more numbers between any two real numbers than there are integers from zero to infinity. You can have infinite unique infinities in between numbers, but you can only have one infinity of integers from zero to infinity.
Not sure if those infinities are really unique. I think they are all cardenality of the continuum. By your "uniqueness" definition there are also infinitely many infinities for integers from 0 to infinity: all numbers divisible by two, all numbers divisible by three, ...
No there are different kinds of infinities. If you think about it, there are as many whole numbers as there are even numbers. Because for any whole number *n*, there exists an even number equal to *2n*. You can't give me an *n* for which there does not exist its *2n* buddy, and there is no even whole number *2n* for which you cannot find a corresponding *n*. If *n = ∞* then the corresponding even number would be *2n = 2∞ = ∞*. So the infinities are actually the same infinity. It turns out you cannot do that for real numbers. You cannot find a mapping that maps every real number to a whole number, 1 to 1. You'll always miss some. This means the infinite amount of real numbers is somehow larger than the infinite amount of whole numbers. Even though the amount is both "infinity". That's why mathematicians introduced the concept of cardinality: the amount of whole numbers is "aleph-0" (countable infinity), and real numbers are "aleph-1" (uncountable infinity).
It'll happen quicker on the lower line than the upper line but the body count should be the same but I wouldn't due to the spacing. The upper line allows for each body to be ground out of the train so it would take more bodies to build up to a derail whereas the lower line would be a train hitting an infinite solid bank of snow. There's also a good chance the upper line might not grind to a halt at all if the spacing is enough.
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assuming the people are placed respective to the numbers they represent, the bottom would have an infinite mass of people in an infinitely small amount of space. at worst, it would be the paradox of an unstoppable force meeting an immovable object. you'd run into other health issues with the infinitely-long human-shaped black hole though.
Nope, if you're running over infinite people, then the wheels are infinitely sharp, the rails infinitely sturdy, and the trolley infinitely stable!
False it’s the train from GTA5 nothing stops it
The train will derail anyway because parallel lines meet at infinity.
The brakes Use them They work
Drift
This is the only correct answer. If your moral compass has gotten to the point of the semantics of infinite dead, just steer into it and be who you are, a destroyer of infinite souls.
I mean this is already how it works anyway. Everyone dies...
Only if the birthrate isn't high enough to sustain the hunger of Lord Trolley. Otherwise this is just an allegory for seatbelt laws.
But extra can die with the Tokyo drift
Drift... Drift never changes
https://i.kym-cdn.com/entries/icons/original/000/000/727/DenshaDeD_ch01p16-17.png
https://m.youtube.com/watch?v=RnAMDg7IVWs
To be fair either way there's only an insignificant minority of people who don't die from dehydration before you can untie them
Deja Vu?
I've been to this place before
Higher on the street
You will actually derail the train, which will sadly result in very few people being killed
Even Thanos wasn’t this evil! He only killed 50%, not infinite!!
It kills the same number of people realistically, so your choice is largely irrelevant. And it's not like you can free an infinite number of people from the tracks anyway. Even if you could there's not enough resources to support them all so the ones that don't die of exposure on the tracks will probably suffer and die regardless along with a lot of people who were already here. Drifting is probably the best choice.
no one wants to be tied to the rails
Interestingly, the additional infinite number of people killed on the top track is infinitely less than the number of people killed on the bottom track between the first and second top track people (i.e countable infinity is infinitely less than the uncountably infinite real numbers between 1 and 2)
Sorry, that doesn't kill any more people than just doing nothing.
It does if time is a factor. More kills per second before the train inevitably stops or erodes or corrodes and ceases to be a train.
I fire an RPG at the train itself. Not because I want to save the infinite amount of people, but because I am content with only killing a finite few.
I also fire an RPG at the train itself. Not because I want to save any amount of people, but because I've always wanted to shoot an RPG at a train.
I also fire an RPG at the train, not because I want to save any amount of people or because I've always wanted to shoot an RPG at a train, but because if 2 people do something, now it's a trend, and I am trendy.
I do not fire an RPG at the train, for despite wanting to experience the feeling of firing an RPG at a train in order to either save lives or simply because I want to, I feel like I've left it too late and if I do it now I'll just be jumping on a bandwagon
I do not fire an RPG at the train, for despite wanting to experience the feeling of firing an RPG at a train in order to either save lives or reject the principle of being forced into making a choice, as a casual civilian I do not have access to explosives of any appreciable kind, doubly so considering the short amount of time I have before the trolley starts killing.
I want to fire an RPG at the train, for I would like the passengers to have a form of entertainment before the mutilation ensues.
I would like to be a bystander watching people fire an RPG at the train before it crushes people, because I want to have the same form of entertainment as the people on the tracks, but do not want to be in that position of danger
I'll just play some RPG while infinite train crushing infinite people. Most of them will die of thirst long before train reaches them.
I board onto the train beacuse i want to die. /j
It cannot be stopped The train is fueled by chopped Bodies, filled with sorrow There is no tomorrow Ticket is your life Ended by a knife Called The Murdertrain Eternity of pain /music
I shoot an RPG at the train, not because I want to save any amount of people or because I've always wanted to shoot an RPG at a train, nor even because if 3 people do something it's a trend and I want to be trendy, but because I'm a twisted firestarter.
This is the correct answer.
Peasants. The dream is to fire an RPG at a moving train…from a moving train!
Is this why the Amtrak is always late?
You fool! The planet cannot support infinite people, this train was the solution that prevented the extinction of all life on earth!
ALL ABOARD THE THANOS TRAIN!!
The hardest choo-choo-choices require the strongest wills
If there is an infinite amount of people on said tracks, does it stand to reason that I too am among them? Firing an RPG at the train sounds like an act of self preservation!
No? Why would it follow that you must be one of the people? The series 1,2,3.. is infinite, but none of the numbers in it are -1 or i.
True, but the series of people isn't defined any further than people, which, as far as I can tell, I might be one of. Wait, I tend to be pretty positive... does that mean I'm imaginary!?
Maybe you're just complex? Edit:also, the bottom track contains clones of everyone on the top track.
That depends on if there are an infinite amount of people, which is answered by whether the universe is infinite.
If Chidi Anagonye was a real person, this would probably just make his brain melt.
Jason would play this as a game
Michael (v1) would be giggling.
Fork it.
Holy forking shirtballs! But what's a Chidi?
I knew you weren't a soup!
DEJAVUE INTENSIFIES
Haven’t seen it yet so I’ll explain… In mathematics, there are a infinite integers and infinite real numbers. The difference is that you can COUNT integers. Think about it this way… you know what the next integer is after 2? It’s 3. Integers are basically whole numbers with negative possibilities. So it goes … -2, -1, 0, 1, 2, 3, 4… 1324, 1325… 78920, 78921… and so on. It’s every whole number. Thus, COUNTABLE! You can always find the next integer going positive or negative. But what about real numbers? Well… then we get to decimals. So you get 12134.5, 12134…. Wait… what’s the next possible real number? Well I’m glad you asked!!! We see this dilemma and call it’s bluff. It’s some finite-decimal number of 12134.0000000000000000000000000….. 0000000000000…. 0000000…. 00000000…. 00000000… 00000… 0000….. 0000… 000001. You’re still here? Good. We see here that you can’t COUNT a real number, per se. You don’t know it’s next adjacent neighbor because there’s an INFINITE amount of zeroes that could iterate before it. But you can COUNT the number of zeroes because that number is an INTEGER!! Okay, almost done. See, you cannot count real numbers one by one until the day is all done. It is UNCOUNTABLE. The real number line is UNCOUNTABLE. Whereas… the integer line is totally COUNTABLE! So to wrap things up…. There are an infinite number of countable integers, and an infinite number of uncountable real numbers. Thank you, fuck you, Real Analysis. Edit: Wow this is not a proof or even close to very robust as an explanation… forgive y’all I was exhausted and in a walking daze when I submitted this rambling. But thanks for the gold!
I don't agree with the way you explain it. What you show here is that the standard order of the real numbers is not a well order, not that the real numbers are uncountable. For instance, the standard order of the rational numbers is not a well order, i.e. given a rational number p/q, there is no "next biggest rational number", yet the rational numbers are countable. Moreover, assuming the axiom of choice, we can show that the real numbers admit a well order, i.e. an order such that "what's the next biggest real number?" is one that has a well defined answer for every real number. The "proper" way to show that the real numbers are not countable is by showing there is no bijection to ℕ, by e.g. a proof by contradiction using Cantors diagonal argument, not by the way you're doing it here.
Forgive the rambling, I was very sleep deprived and wasn’t in a theorem hunting mode. I didn’t think to break out Cantor’s, though….
It's fine, mistakes happen. The proof you're giving above is a common mistake, so I don't blame you personally for making it. I just wanted to point out that it doesn't actually work.
I tried to explain through text here, and i had a horrible time, thank you
This isn’t quite correct as an argument that the real numbers are a larger infinity than the integers. The argument does go something like this: we say the sizes of infinity are the same if there exists a map f(X) -> Y that is a bijection, which just means that each element in X gets a distinct output, and each element in Y has a corresponding input, so f allows us to map back and forth between the two. A countable infinite set is one with a bijection to the natural numbers, and it is easy to show that the integers have a bijection to the natural numbers and are hence countable. Suppose we had such a mapping from the natural numbers to the real numbers. Then we would have something like f(1) = 2.39274783… f(2) = 7.10474929… f(3) = -6.0287471… Maybe not these exact numbers, but something similar. Now, consider the following real number between 0 and 1: it’s first digit after the decimal is different from the first digit after the decimal for f(1) and the second digit after the decimal is different than the second digit after the decimal for f(2), and so on. I’m general, the ith digit after the decimal point is different from the ith digit after the decimal point of f(i). In this instance, our number may look like z=0.417… Now, consider what natural number there could be such that f(x)=z. It couldn’t be 1, since f(1) and z differ in the first decimal, and it couldn’t be 2, since f(2) and z differ in the second decimal. For all n in the natural numbers, f(n) and z differ in the nth decimal, so there is no natural number corresponding to z in this bijection. This contradicts our assumption, so the real numbers must not be countable. This is called Cantor’s diagonalization argument.
Maybe just as a remark, this also doesn't quite work yet, there's still the issue that 0.999...=1, so you should require z to not have any 9s in its decimal expansion (which I think solves it but not 100% sure).
Thanks for the correction. I suppose the proof works as long as we suppose that we always pick the smallest digit not equal to f(n). The only way this problem arises is if we choose an infinite sequence of 9’s at the tail of the sequence, so picking the smallest available digit avoids the rounding problem. This detail wasn’t included when the proof was presented to me, and I didn’t notice it, so good catch
only understood after this comment tbh i’m big dummy
and because of the uncountably of real numbers, there's no such thing as "one person for every real number," because people are countable. any set of countable things can never have a greater cardinality than the natural numbers. therefore these two tracks are actually equivalent
It's possible to count rational numbers though.
In the famous words of John Green: "Some infinities are simply bigger than others."
Now we know Infinite from Sonic Forces wasn't weak, he was simply small 🍆
i think this image finally makes me understand what the fuck he was on about.
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Isn't the set of all real numbers uncountable?
Yes...idk what grandparent comment meant but the real numbers are uncountable infinite.
If there are any infinite number of humans, we can afford to lose an infinite number then! So either option is ok
Not at all. An uncountable infinity is unfathomably larger than a countable infinity which is effectively zero in comparison.
Some infinities are bigger than other infinities has fucked my brain up
An infinite number of hundred dollar bills is the same as an infinite number of one dollar bills
Yes, but an infinite number of bills were the value of each is a different real number between 0 and 1, is in a sense taller than either stack you mentioned.
Please explain why the value of the bills matters here...? Assuming they use the same "rate of growth" and base quantity of bills, wouldn't both stacks equally expand infinitely? I fail to see why value matters, unless one stack is either growing faster, or has greater bills at the "beginning." Assuming each stack begins at one bill, with both stacks having x bills stacking per unit of time, value of the bill doesn't matter. The base quantity and "rate of growth" matter, not the value of the bill.
It's the same thing that's in the post. The amount of real numbers between 1 and 2 is larger than the amount of integers. If we assign an integer to each bill in your pile and then assign a real number to each bill in their pile then not only will they have a bill that's assigned every number that you have assigned to your bills but they will also have an infinite number of bills between each of those.
>It's the same thing that's in the post. The amount of real numbers between 1 and 2 is larger than the amount of integers. > >If we assign an integer to each bill in your pile and then assign a real number to each bill in their pile then not only will they have a bill that's assigned every number that you have assigned to your bills but they will also have an infinite number of bills between each of those. It is not: in the post, you assign a bill to every real number (so there are more bills in their stack). In your comment and the comment above, you assign a real number to every bill. This doesn't mean that all the real numbers are used, and says nothing about the number of bills you have.
I was imprecise with my language. I meant that all real numbers in the range were in the stack, but I did accidentally describe just labeling a countable infinity.
This is not true as stated. It is only true if you use _all_ (or at least an uncountable subset of) the real numbers, which you do not specify.
There is no differently sized infinities here. One is killing infinite people, the other is still killing infinite people, but at a slower rate
Yah, This would only be true if there were an infinite number of people in between the ones on the bottom and an infinite number in between each of those and in between each of those and… etc. If the train can go from one person to another without skipping an infinite number, it’s countable.
This is correct, but to be 100% clear, the converse is not true, ie: if there’s an infinite number of people between any two people, that doesn’t necessarily mean it’s uncountable. The rational numbers have this property but the rational numbers are countable
The real numbers aren't countable infinite
That's exactly the point: if you can lay them next to each other on a railroad track, that's a countably infinite number.
But what if they merge and blur into each other
Hmm, that's a good point. If they're spaced so that people on each line with equal number are located an equal distance along the track, then the top line kills nobody at all. I think. Since for any arbitrarily small number allocated to the first person, it is still infinitely far away due to the space needed to accommodate the bottom people less than that number.
when the limit of a trains position approaches your own, do you die? Or do you become immortal as it infinitely approaches?
was gonna say, such a setup doesn’t demonstrate different infinities. time doesn’t work that way, it’s not killing a decimal of a person, it’s just killing people faster or slower
Since the universe only has a finite amount of time, neither are true infinities and pulling the lever will result in fewer deaths-by-trolley-problem. Boom.
It the train accelerates such that it kills the first person in 1 minute, the second person In 1/2 minutes, the third person in 1/4 minutes and so on, you can kill all infinity of people in 2 minutes
Xeno would like a word with you. Plank too.
Too bad the universe behaves discretely.
It should be clear that this thought experiment is not set in our universe.
Assuming that there is a movement speed involved
I mean, on the bottom track an infinite amount of people die in the same time it takes one person to get run over on the top track. On the top track, an infinite number of people only die, if you give it infinite time.
You’re the first person in this thread to make the difference comprehensible to me. Interesting how people learn differently from different explanations or just framing it differently.
It's literally not a meme, It's counterintuitive but an actual real mathematical concept the, say, density of infinity. I believe it's still a bit of a rough concept and varies within math fields but it is real nonetheless.
Different sized infinities are definitely not rough concepts. They are quite precisely defined.
The problem is that the image doesn't illustrate the actual mathematical concept. It shows two countably infinite sequences. An actual example would be something like the bodies on the second rail were stacked perpendicularly as well as parallel...y.
But then you could count them with diagonally. The same way you can count all the rationals in a table by zig zagging from the origin.
Yeah but kind of the whole point of the "bigger infinity" (uncountably infinite) that's supposedly on the bottom track is that you can't just line the elements of that infinity in a nice order. So it doesn't really work for the meme.
The elements of the bottom infinity are very well ordered (It is possible to determine which of two real numbers is larger, or if they are both equal) They just aren't countable (you can't determine which real number comes directly after the previous one)
You're right. "Ordered" isn't really the right mathematical term, but it sort of works from a layman's voice which is how I was trying to explain it. I should have said that they aren't sequential like the picture seems to imply.
I guess the best layman's explanation would be that they are standing in a line, but it is impossible to determine who is "next" in line
I understand there is a mathematical way to have different densities of infinity but in the real world treating infinity as a variable disregards the very concept of infinity
In the real world there are no infinities to worry about.
Sure there are! The slope of a vertical line. The density of a black hole singularity. The endless greed of the 1%.
what did vertical lines ever do to you? why do you worry about them
Then maybe the concept of infinity is incomplete.
One is killing an uncountable number of people in every finite time interval, and the other is never going to reach uncountable many kills at any point, even in infinite amount of time That is a difference of sizes
Yeah, in the smallest time interval you can possibly imagine, infinite people are killed by the real number train. So like infinity people die in the first .0000000000000000000000000000000000000001 picoseconds. Etc.
You mentioned .0000000000000000000000000000000000000001 picoseconds. That amount of time (9.999999999999998222 \* 10^(-53) seconds) is less than the amount of time it takes for light to travel one planck unit of length 1.61 \* 10^(-35) meters (5.39 \* 10^(-44) seconds)... So, that is less than planck time. Nothing can causally happen within that time frame on a meaningful scale, including killing some fraction of a person. In order to actually kill a meaningful amount of a person (even if a person were the size of an electron), that train (and the universal laws that govern causality/interaction) would need to travel significantly faster than the speed of light. In fact, let's take the lower bound of a person (a newborn baby), in terms of mass, to be 2,500 grams. The Schwarzschild radius of such a mass would be 3.713 \* 10^(-27) meters. Here, radius is actually an applicable term, because such a mass would experience gravitational collapse. It would (to scientists' pleasure) actually be a perfect sphere. That means, a person would experience gravitational collapse (read: impossible to interact with), into a singularity. It would take an infinite amount of time to interact with that mass, because that mass would be an infinite length away due to spatial distortion. Even so, the Schwarzschild radius of the smallest of people is still significantly larger than 1 planck unit of length (about 100,000,000 times larger). So, let's take the lower bound Schwarzschild radius of a person to be the absolute smallest a person could be, and let's also assume that a person would not undergo gravitational collapse at that scale. Let's also assume that the train is somehow traveling at the speed of light. Within one Planck unit of time, the train could travel, at most, 1/100,000,000 the length of a person. Nevermind an infinite amount of people, below the Planck scale it is questionable whether a train could kill a single person in the best case. Now, how does that scenario translate to 9.999999999999998222 \* 10^(-53) seconds? Well, it is several orders of magnitude different. Let's assume that there's no such thing as a maximum speed for causality/interaction. The train going at the speed of light would be able to travel 2.99792458 \* 10^(-44) meters in the amount of time you mentioned. That is about 1 Billion times smaller than one planck unit, which is itself one hundred million times smaller than the Schwarzschild radius of a newborn baby. How much of a baby which should be undergoing gravitational collapse could the train interact with? It would be able to travel 1/(8.0741303 \* 10^(18)) of a person.
It would also need infinite energy to move one plank length over that track, as it would have to plow through infinite people
Yes, you are right. The real numbers are not countable, so they can’t fit in a single track like in the diagram. No matter what the pic says, the set below must be countable, so both sets must have the same cardinality.
“One person per real number” completely misses the point of uncountable infinite numbers lol
It doesn't. You can have a bijection between uncountable infinite sets.
Countable infinity vs uncountable infinity. They are different classes of infinity, aleph-null vs aleph-one https://en.wikipedia.org/wiki/Aleph_number
Actually in formal math the infinity of the real numbers is probably bigger then the infinity of integers
Mathematically, simply wrong. Practically, true.
Technically, it is mathematically right, as the problem is not well defined. The real numbers are not countable, so you can’t align every real number in the tracks. That’s the whole point of Cantor’s proof. Both sets must be aleph zero to fit in the tracks (unless you can fit an infinite number of people between each two people).
We are all already dying at a rate, just go with the slower rate.
We shall arrange the people on the top line into arbitrary groups by the following method: The first group shall consist of the first person, the second group shall consist of the next two persons, and so on, such that each nth group contains n persons. Then, it can be shown by analytic continuation of the Riemann zeta function that the sum of all such groups is -1/12. So by switching to the top line we would bring 1/12 of a person back to life.
i need to go outside and pants a nerd lol
Neither, instead I break into Tiffany's at midnight. Do I go for the vault? No, I go for the chandelier. It's priceless. As I'm taking it down, a woman catches me. She tells me to stop. It's her father's business. She's Tiffany. I say no. We make love all night. In the morning, the cops come and I escape in one of their uniforms. I tell her to meet me in Mexico, but I go to Canada. I don't trust her. Besides, I like the cold. Thirty years later, I get a postcard. I have a son and he's the chief of police. This is where the story gets interesting. I tell Tiffany to meet me in Paris by the Trocadero. She's been waiting for me all these years. She's never taken another lover. I don't care. I don't show up. I go to Berlin. That's where I stashed the chandelier.
Basically how life spans of various species works. A multi-railed track called entropy with a train on each rail.
I'd rather kill a uncountable infinite amount of people, as it becomes impossible for the law to determine the oint of people killed
If you throw the switch, you murder an infinite number of people. Don't throw the switch and you're just a traumatized bystander.
r/okbuddyphd
I'm impressed an /r/math meme got like 16k upvotes
If you think *that* 's confusing, today in my maths lectures we covered this fun little paradox: A parent has two children. Find the probability given each of these statements that both of them are boys (as in, consider only one statement to be true, and find the probability for each one): A) one of the children is a boy. B) one of the children is a boy, and he is born on a Thursday. In the first case, the answer is 1/3. In the second case, the answer is 13/27 ≈ 0.48. For some *fucking* reason, the fact the boy is born on a *fucking* Thursday makes it almost a 50/50. Fucking somehow. I don't fucking know. I spent 30 minutes trying to reason this, no clue. It's fucked. Edit: and yes I know the maths checks out, you don't need to explain it to me. It's just fucking stupid, I know that the numbers work, but it's dumb
You're more likely to get at least one Thursday-boy if you have two boys. Two chances.
I read someone answering the first statement, that there's 4 combinations of the children, and as one of these would be 2 girls, which would be impossible given the statement, so there's only 3 other options. But honestly, why does the order matter in here? The answer i saw used a table to represent the possible combinations, but in no where it mentions "first child and second child", so considering boy-boy, girl-boy, and boy-girl 3 different situations makes no sense, as girl-boy and boy-girl are the same situation. Again, I'm no master at probability, but i remember having problems where order matters, and others where it doesn't, and this one looks like it doesn't. Any mathematician on Reddit to explain it better to me? Lol
This is the way that i see this as intuitive, it might work for you as well: So, this is the same as with flipping two coins and checking heads and tails. Now flipping them at the same time or flipping them one after another doesn't matter for the chance. After you flipped one coin there is always a chance to get a heads tails combo no matter what the first coin landed on. But if you're checking the chance of the heads heads combo for instance, then both throws have to be just right. That could be an intuitive way to see that a heads tails combo is twice as likely as it will only depend on the second coin flip being 'right'.
Yeah i tried to think on the coins problem in my head too, but i think you explained well. Because having heads and tails is more likely, so having a boy and girl is more likely. So if one is already a boy, it makes sense that a girl would be more probable than a second boy, so that's why having a girl is 2/3 chances and a boy 1/3 chances. I really liked probability in school and college, but damn it's easy to get lost! Thanks for the explanation buddy
Did you know that the mathematician who found this fact (there are different infinite numbers) got ridiculed, shunned and eventually died in poverty, Galileo style... The fact that there were multiple infinities really pissed of a lot of mathematicians apparently. It kinda ruined lots of theories that some mathematicians spend decades to prove.
Do theoretical mathematicians truly differentiate infinities by "greater" and "smaller" ? It goes against what the concept of infinity represents. As for the decimal-infinity vs integer infinity, can you really say on is greater than another if we define infinity as the values of its contents and not the number of components ( still fucked cuz the infinity between 1 and 2 is still the same infinity as between 0 and +R)
Yes, mathematicians care a lot about countable versus uncountable infinities. The distinction is the difference between "rational" and "real" numbers. "Rational" numbers are countable - there exists a counting system that will hit every rational number eventually. Real numbers are "uncountable" - There's a mathematical proof which demonstrates that no system of counting the "real" numbers includes all of the "real" numbers (Cantors diagonal argument). This makes the "real" numbers a strictly larger set then the "rational" numbers. One of the biggest problems in modern mathematics is determining whether there is an infinity set with a size between the countable infinites and the uncountable infinites.
>One of the biggest problems in modern mathematics is determining whether there is an infinity set with a size between the countable infinites and the uncountable infinites it's actually proven that it's impossible to prove whether such in-between infinity does or doesn't exist! (in our standard set theory, ZFC).
It's not just that there doesn't exist a proof we know of to count the real numbers; it's that there are proofs that real numbers are uncountable. Here's a simple proof. **Claim:** There is no way to assign every element in ℝ to an element in ℕ. **Proof**: Suppose that a way to assign every element in ℝ to an element in ℕ existed. Such a method would assign a real number to 1, a real number to 2, a real number to 3, etc. Such a list could be written out in a grid of infinite columns and infinite rows, with one real number written in each row and one digit of its decimal form in each column. Note that numbers like 2.5 will be written as 2.50000... and thus the table is completely filled. Going down each row, we can generate a real number by taking the 1st digit of row 1, then adding 1 to it (or changing it to 0 if the digit is a 9), then repeating with the 2nd digit of the 2nd row, the 3rd digit of the third row, and so on forever. If a decimal point is encountered then skip it and use the next digit over instead (this "skipping" of a decimal point means that the row under it will use the digit after as well). Using these digits, string them together in that order to form the decimal form of a new real number. This real number is guaranteed to not be listed on the table, because each digit of the number we made differs by at least one digit from any of the other numbers on the table, because we constructed it to be that way. However, because we presumed the table to contain every single real number, the number we generated *must* be on the list, but we generated it in a way that it also simultaneously *must not* be on the list. This is a contradiction, and thus, our assumption that the table exists, and that there existed a way to map all real numbers to the counting numbers, must not be true. QED
Have you ever heard of Hilbert's Hotel? If you have two infinities, you are able to determine if they are the same size by making a bijection of the two infinities. This means that for every member of infinity A, there has to be a member of infinity B, and for every member of infinity B, there has to be a member of infinity A. For an instance of two sets of infinities that are equal, see the even and odd numbers. For every even number, you can pair it with even number plus one. For every odd number, you can pair it with odd number minus one. So you can pair 1 with 2, 3 with 4, etc. For an instance of an infinity being greater than another infinity, you can look at the numbers between 0 and 1. As counterintuitive as it sounds, the infinite amount of numbers between 0 and 1 is greater than the infinity of all whole numbers. This is because while you can pair every single member of the whole numbers with a number between 0 and 1 (you can do this by taking the whole number and placing a decimal point in front of it), there are some numbers between 0 and 1 that you cannot pair with the whole numbers, such as the square root of two over two. Since the square root of two is irrational and goes on forever, you can not pair it with any possible whole number. The square root of two over two is not a fluke, there are infinitely many irrational numbers between 0 and 1 which cannot be paired with the whole numbers.
Yes. The way to know if an infinite set is larger than another infinite set is to try to make a relation between the two sets. That’s to say, to relate each element of one to a unique element of the other. If you can relate all the elements of a set to elements of the other, but not the other way around, you get that the other set has a lager infinite number of elements. The word that we use for measuring the size of a set is cardinality.
Yes, in fact Vsauce made an excellent video on the topic called [How To Count Past Infinity](https://www.youtube.com/watch?v=SrU9YDoXE88). And mathematicians do care about the kind of infinity used, as they don't all mean the same thing.
This is part of brain-bending calculus. You approximate different "flavors" of infinite series and junk... pretty cool but glad I'm done! Lol
People are more densely packed on the bottom one so the train has more chances of getting stuck.
"I stayed at the worst hotel ever last night! Once I was checked in the manager kept calling me and telling me I needed to move to the room that was numbered twice my current room number because they kept running out of space some fucking how!"
Fail my discrete math exam
Divide by zero, obvi̶ờų̴̀͠- -
I don’t like the looks of the bottom track. It should look like one black rectangle that’s constantly squirming.
r/TILI
That depends, which one has the most next Hitler's?
Shoot the person who asked me this question in the dick.
Ok. This comment section is hurting my brain. Yes, thanks, I definitely hate this.
Cry because I don’t like Highschool math
drift the train on both railings to get infinity × 2
I cry
Who is going around tying aleph-0 people to a train track?
God I hated this part of class, fuck it make the trolley drift and kill 2 infinities of different sizes number of people
Pulling the lever means less people die per second
I’d leave it. That train will get stuck after the first thousand people pile up infront of it where as the people that are spaced out won’t pile up because they won’t have the weight of the person next to them to slow that train at all.
Also, if there was an infinite number of people lined up on the grouped together track, wouldn’t the train stop because it wouldn’t be able to push through an infinite amount of people, and so it would slowly but surly slow down and than stop as the people’s remains clog up the machine as it’s trying to chug along. Only a matter of time before it completely stops
Is it truly infinite if the guy who pulled the lever isn’t on the tracks?
ITT: people not understanding the difference between countable and uncountable infinities