/sci/ - Science & Math

[Anonymous No.9736243]

The top track is an infinite set of people A = {1,1,1,1,1,...}
The bottom track is an infinite set of people B = {1,2,3,4,5,...}

Which set has the highest absolute value, and which lever should you pull?

[Anonymous No.9736248]

[Anonymous No.9736250]

In the end the two choices will kill all the people in the world

[Anonymous No.9736252]

The lever to A. Even though both are infinite, B still has more elements. Just like the set of real numbers is more dense and contains more numbers than the set of naturals even though both are infinite.

[Anonymous No.9736256]

>>9736243
kek i remember making this picture like 2 years ago. good times

[Anonymous No.9736259]

>>9736252
>>9736250
Undergrads detected
Sci is dead

[Anonymous No.9736260]

>>9736259
they're both countably infinite, right? the only difference would be the rate at which people died

[Anonymous No.9736261]

whichever lever makes the train run me over

[Anonymous No.9736262]

We know that [math]\sum^\infty n = -\frac{1}{12}[/math]

Adding the two series term by term, we have

[math]\sum_{n=1}^\infty n + \sum_{n=1}^\infty 1 = \sum_{n=1}^\infty(n+1) =\sum_{n=2}^\infty(n) = -1 + \sum_{n=1}^\infty n = -\frac{1}{12}-1 = -\frac{13}{12}[/math]

This shows clearly that by multi-track drifting, you kill the least amount of people, making it the utilitarian correct choice.

[Anonymous No.9736264]

>>9736262
wtf i love set theory now

[Anonymous No.9736276]

>>9736262
the tracks diverge so multi-track drifting is not possible unless the trolley expands endlessly

[Anonymous No.9736278]

Suppose the train smashes one "group" of people every second. For any given time [math]t[/math], the integer [math]n\;=\;\left\lfloor t\right\rfloor[/math] indicates the number of groups the train has smashed so far. First, two lemmas have to be proven. The number of all people on the upper rail up to [math]n[/math] groups is
[eqn]\sum_{i\;=\;1}^n1 \;=\; 1 \,\times\, \left(n\,-\,1\,+\,1\right) \;=\; 1\,\times\,n\;=\;n[/eqn]
and the number of people on the lower rail up to [math]n[/math] groups is [math]\sum_{i\;=\;1}^ni[/math] which can be derived in closed form in a simple way. For any natural integer [math]n[/math],
[eqn]2\,\sum_{i\;=\;1}^ni \;=\; \sum_{i\;=\;1}^ni \,+\, \sum_{i\;=\;1}^ni \;=\; \sum_{i\;=\;1}^ni \,+\, \sum_{i\;=\;1}^n\left(n \,+\, 1 \,-\, i\right) \;=\; \sum_{i\;=\;1}^n\left(n \,+\, 1\right) \;=\; n\,\left(n\,+\,1\right) \qquad\text{therefore}\qquad \sum_{i\;=\;1}^ni \;=\; \frac{n \,\left(n\,+\,1\right)}2.[/eqn]

The difference between the number of people smashed at [math]t[/math] were the train to go down and were it to go up is henceforth
[eqn]\sum_{i\;=\;1}^ni \,-\, \sum_{i\;=\;1}^n1 \;=\; \frac{n\,\left(n\,+\,1\right)}2 \,-\, n \;=\; \frac{n\,\left(n\,-\,1\right)}2 \;\geq\; 0.[/eqn]
Therefore, no matter how long the train continues before stopping, fewer people will die if you pull the lever.

[Anonymous No.9736281]

The bodies in set B might eventually be densely packed to put a stop to the trolley permanently, if so B

[Anonymous No.9736284]

The top track is clearly filled with clones

[Anonymous No.9736286]

>>9736256
No I made it :)

[Anonymous No.9736288]

If you iterate through an infinite set can it really be called infinite? No matter how long the trolley runs over people, it will never run over an infinite amount of people
So would it be more correct to call the set "infinite" or just "continuous"?

[Anonymous No.9736290]

>>9736286
>>9736256
stop claiming credit for my OC :^)

[Anonymous No.9736291]

zeta(0) = -1/2
zeta(-1) = -1/12

Therefore 1 + 1 + 1... will resurrect half a person, and the second one will only a twelfth.

[Anonymous No.9737739]

>>9736252
>Even though both are infinite, B still has more elements. Just like the set of real numbers is more dense and contains more numbers than the set of naturals even though both are infinite.
go back to numberphile

[Anonymous No.9737751]

>>9736288
Consider that our universe itself is not infinite.
Therefore at some point in time the trolley will stop, no matter how long the lines are. At this time track B will have a higher kill count.

So as answers, both sets are equal and you should pick track A.

[Anonymous No.9737758]

>>9736248
Don't pull it. Fuck those people.

[Anonymous No.9737772]

>>9737751
>Consider that our universe itself is not infinite.
Oh? Where's the boundary?

[Anonymous No.9737785]

>>9737772
Heat death or possibly a big crunch.

[Anonymous No.9737789]

>>9737772
You're a fucking moron.

Read some Aristotle or Hawking. Nothing physical is infinite.

[Anonymous No.9737834]

>>9737789
prove it, pussy

[Anonymous No.9737835]

>>9736243
Ultimately they have the same number of people since there are an infinite number of elements in both sets and the sets are the same length, but if you consider that the train travels at a constant rate then the rate of deaths is constant for track A and increasing for track B.

Therefore choose track B

[Anonymous No.9737841]

Kill as many people as possible. The only moral good is to murder.

[Anonymous No.9737842]

>>9737835
nice

[Anonymous No.9738265]

>>9736243
I pick the track with the hottest girl then tell her I picked the track because of her, because I don't place value in masses of humans. At the moment a mass population death would be beneficial.

[Anonymous No.9738424]

>>9736262
this

[Anonymous No.9738434]

>>9738265
This

[Anonymous No.9738438]

>A = {1,1,1,1,1,...}
So, A={1}? Learn how to fucking write sets.

[Anonymous No.9738451]

>>9737834
Actually, the onus of proof is yours.
Since your statement is the one that is not falsifiable.

[Anonymous No.9738460]

the tracks diverge. multi-track drift so the train will derail and crash after killing less than 10 people

[Anonymous No.9738477]

>>9738460
Run it over track A. They may both be infinite, but if the train's velocity is constant, track B will always contain more individuals than
A as n approaches infinity.

[Anonymous No.9738487]

>>9736243
There's a bijection for both A and B tracks; therefore card(A)=card(B).

It doesn't matter which track you choose. The same number of people die.

[Anonymous No.9738491]

>>9738477
>They may both be infinite
You mean to say countably inifinite.


>track B will always contain more individuals than
A as n approaches infinity.

If sets A and B were finite, your argument would be correct, but because sets A,B are both countably infinite, their size is the same; therefore, as time approaches infinity, you will have killed the same amount of people either way.

[Anonymous No.9738498]

>>9738491
Nah, infinity doesn't exist as a concrete point in time, and unless the two sets stop getting larger at some time (I.e., they "converge" to some sum of people), set B will always be larger than A

[Anonymous No.9738502]

>>9738491
Your mistake was not realizing that time limits the number contained in each set. I.e., a set can never be bigger than it is at t=0 until t=1, etc

[Anonymous No.9738504]

this fucking thread is going to last for a week

[Fuck you No.9738512]

>>9736243
>infinite set of people

This makes no sense. Your question is as retarded and related to ACTUAL MATH as talking about mermaids is related to biology.

Think about actual math and stop fantasizing with useless and retarded concepts.

[Anonymous No.9738848]

>>9738502

You're right for any particular time t.

However, I'm talking about time approaching infinity. As time approaches infinity, the cardinality of the sets will also approach infinity.

[Anonymous No.9738850]

>>9736259
retard

[Anonymous No.9738852]

>>9736243
Lever B because it'll probably stop the trolley

[Anonymous No.9738867]

>>9738498
>Nah, infinity doesn't exist as a concrete point in time,

I agree that the expression t = infinity is meaningless. However, t -> inf is not meaningless.

>unless the two sets stop getting larger at some time (I.e., they "converge" to some sum of people)

The cardinalities of these sets do in fact converge to some particular size; we call this size countably infinite.

as t -> inf, then

card(A) = countably infinite
card(B) = countably infinite.

[Anonymous No.9738868]

>>9737751
But where in the OP did it state that the universe was the end of the otherwise infinite set?

[Anonymous No.9738911]

There are only [math]-\frac{1}{12}[/math] people on the bottom track.

[Anonymous No.9739008]

>>9738451
You have no way of proving or disproving that the universe is finite either. The value of c prevents you from interacting with the universe, if it exists, beyond the light boundry.

[Anonymous No.9739012]

>>9736252
ohh god...

[Anonymous No.9739103]

>>9736262
The more you know

[Anonymous No.9739179]

>>9738867
>cardinalities of these sets do in fact converge
What topology on the (large) set of cardinals are you using?

[Anonymous No.9739293]

>>9736243
Will the train continue infinitely?

[Anonymous No.9739323]

>>9736243
neither of those are sets unless we understand the first one to be the singleton {1} or both of them to be functions from N to itself,

{(1, 1), (2,1), (3,1), ...} and {(1, 1), (2, 2), (3,3), ...}.

Absolute value defined on sets (or multisets) is... well, not defined. Obviously both sets have the same cardinality and the sum of the elements of both sets is divergent, but if we're talking in the context of ordinals the limit of both sums is omega, hence still equal. You'll have to give more info if you want this question to have an answer

[Anonymous No.9739339]

>>9736243
Both sets have measure zero. It doesn't matter which lever you pull.

[Anonymous No.9739361]

>>9738848
This is why infinity is an absolutely meaningless concept. As t tends toward infinity the sets are infinite, but we can't say anything about their size except at a particular time t if we want any meaning. Even still, assuming the train speed is constant, at the point of infinity, both sets may contain infinitely many, but it's clear set B will contain more than A. Their cardinalities are not equal

[Anonymous No.9739363]

>>9738512
>reddit spacing
>>>/out/

[Anonymous No.9739364]

>>9736243
niether

it would be immoral to decide the destination of the truck and who dies/not dies

the only moral way is to not be involved in the decision.

[Anonymous No.9739368]

>>9739363
not same poster -
a) who cares on this board if someone has been on reddit?
b) why is that "spacing" exclusive to reddit?
c) why arent you on your containment board?

[Anonymous No.9739398]

>>9736243
Simple arithmetic.
[math]A + B = (1 + 1) + (2 + 1) + (3+1) + ... = 2 + 3 + 4 + ... = B - 1 \\
A+B = B - 1 \implies A = -1 [/math]

This means that by killing all of the members of set A, you are killing -1 people and thus bringing someone back to life.

[Anonymous No.9739431]

god /sci/ is so bad
at least make trolley threads ironic

[Anonymous No.9739434]

[Anonymous No.9739438]

[Anonymous No.9739441]

[Anonymous No.9739442]

[Anonymous No.9739446]

[Anonymous No.9739448]

[Anonymous No.9739450]

[Anonymous No.9739453]

[Anonymous No.9739461]

>>9736243
I would set the lever to A because theres an obvious time constraint per kill because of how spaced out they are. The rest of the question is Sudoku level tier retardation.

[Anonymous No.9739468]

ITT

accessories to the fact of murder

[Anonymous No.9739471]

>>9739431
Unfunny meme as a bijection exists between the two tracks meaning that the cardinalities can't be different.

[Anonymous No.9739475]

[Anonymous No.9739476]

[Anonymous No.9739490]

>>9739475
ROFL TYSM

[Anonymous No.9739493]

>>9739476
OMG these are hilarious

[Anonymous No.9739506]

[Anonymous No.9739510]

>>9739506
who needs 3 terms when there is this :D

[Anonymous No.9739545]

>>9736243
If track a is infinite niggers and track b is infinite whites the the most ethical is track a

[Anonymous No.9739550]

>>9739545
HAHA TRICKED YOU ANON!

The lever was electrified! Enjoy!

[Anonymous No.9739722]

>>9739475
Don't touch the lever duh

[Anonymous No.9739723]

>>9739476
based

[Anonymous No.9740620]

>>9736262
>We know that [math] \displaystyle \sum_{n = 1}^\infty n = \frac{-1}{12} [/math]

...

[Anonymous No.9740653]

>>9739438
ftfy

[Anonymous No.9740967]

>>9736243
haha if i have infinity feathers and infinity rocks what weighs more

[Anonymous No.9740978]

>>9736243
Track A; it kills a positive amount of people. ;^)

what about pic related?

[Anonymous No.9740984]

>>9736243
With no limit or range: both are the same
With a limit: it depends fucko

[Anonymous No.9740989]

>>9736243
Don't pull any lever and walk away with a sense of morality that you didn't get yourself involved with killing and having the power of life or death over an infinite amount of people.

Let it RIDE!

[Anonymous No.9741001]

>>9736243
I'd chose B because fuck people but if you want to know the math just take a calc 2 course or read a text book

[Anonymous No.9741010]

The first set has cardinality 1 so I'd take A.

[Anonymous No.9741012]

>>9741010
are you retarded?

[Anonymous No.9741017]

I put a double slit at the junction so that both everyone and no one is run over.

[Anonymous No.9741026]

>>9741017
love this answer

[Anonymous No.9741040]

>>9741012
Are you? |{1}| = 1

[Anonymous No.9741105]

>>9736243
Multitrack drifting

[Anonymous No.9741277]

>>9736243
Track B because it will result in a net total of [math]-\dfrac{1}{12}[/math] people dying, while the top one results in an infinite amount of people dying

[Anonymous No.9741298]

>>9741010
Yeah, I noticed this too. OP should learn his real analysis ;^)

[Anonymous No.9741647]

>>9736262
lmao

[Anonymous No.9742915]

>>9737739
Care to explain how he is wrong instead of spouting memes?

[Anonymous No.9742918]

>>9736243
Top track is less deaths, its still infinitely many but kills at a slower rate, after ~100 years everybody on the tracks will already be dead.

[Anonymous No.9743506]

>>9742915
The mapping of set A to set B is bijective

[Anonymous No.9743521]

>>9742918
FAKE NEWS

Everyone tied to the track will be dead in about 3 days due to dehydration. More if they can cannibalize to some extent.

I would choose to mercy kill as many people as fast as possible so they won't have to suffer for the full three days

>t. Thanos

[Anonymous No.9743537]

>>9736243
At any point in time the top track will have less people killed. Infinite time will never pass, so this holds for all eternity. The choice is pretty obvious.

[Anonymous No.9743601]

>>9736252
I just threw up.

These two sets are both countably infinite, hence the same size. They have the same amount of elements. The real numbers, on the other hand, are uncountably infinite thus a larger infinity.

Please refrain from talking about things you don't know about, thanks!