I'm bored

I'm bored.
So bored.
We should make a puzzle.
Does anyone have a puzzle?
Puzzles are nice.
Or, maybe some kind of small challenge? Something that seems difficult until you understand it more thoroughly?
Ugh. How do you stop being bored, user?

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Ich bin dabei

Wouldn't the balls just stay in the second cup? It's not angled in any manner that would cause them to just go into the third cup.

Tis a gif, friend.

though, I think you're right. If anything, they'd lead to the second cup realistically.

They would, but then they would just stay there.

I have autism, please be patient.

Consider the following:

> There is a vase that is empty
> At each step, I put in 10 marbles, and take out 1
> Each time I do this, I reduce the amount of time I wait before doing it at again by half
> So 10 in 1 out, wait an hour, 10 in 1 out, wait 30 minutes, 10 in 1 out, 15 minutes, and so on.

How many marbles will be in vase after 2 hours?

Why not just put in 9 marbles?

Its part of the puzzle, Mr. Trips

An infinite amount.

kek

Go home, Zeno, you're drunk.

Well, if the person doing this does so exactly as stated, they obviously have a mental compulsion to do so, and thus, shut the fuck up.

Let's say I number the marbles. 1, 2, 3, and so on.

I put in marbles 1 - 10, and then I take out 1. Next I put in 11 - 20, and then I take out 2. 21 - 30, I take out 3.

Thus, at the end, I will have taken out every numbered marble. So it must be empty.

And since you speed up to half every time you do it, you are taking out twice the marbles by the time you would normally take out the marbles, and only be putting in more.

9 in 1h (1h) +
9 in 30m (1.5h) +
9 in 15m (1.75h) +
9 in 7.5m (1.875) +
9 in 3.75m (1.9375)

Hmm.
Seems like the number of hours is going to be
1 + 1/2 + 1/4 + 1/8 + ...
And the number of 9's multiplied together is going to be the number of terms?

I never really fiddled with this stuff before. I watched a yt video like, a couple years ago at least but I can't really remember any of it.
Thanks, user.

You never reach 2 hours cuz 1+1/2+1/4+...

No you'll always have 9 times more in than you've taken out, wait how many marbles does this vase hold anyway? No you know what, fuck you and your stupid ass puzzle, that guy says right you may aswell just put 9 marbles in, and the other guy was right to say infinite and you're trying to explain your pathetic puzzle that's already been simplified and solved in a way that confuses people so fuck you, your puzzle was and still is a shit idea.

bullshit.

This is samefag who made the puzzle, can't believe it's just a random dumbass.

He's right.
You put in more than you take out, but since you put in /part/ of what you take out, as it reaches infinity it doesn't matter. Because they're both infinity.. You're taking infinity away from infinity, which equals 0?

Huhm.

Don't feel bad user, There's always a job for you at McDonalds.

TIL: I am zeno.

There are different levels of infinity though of you always add 9 everytime you take one out you will never be left with 0

this shit is only applicable in an arbitrary base 10 counting system, has nothing to do with actual math.
This would be a riddle, not a puzzle.

also lame

...

I'm a network engineer, and your shitty logic would be shot down fast where I work lol

thats more like it

I'd think they both become infinite.
One /feels/ like it should be bigger, but if you have a set of 1, 2, 3, 4, until you get to infinity, that's the same size as 2, 4, 6, 8, to infinity.
Because you could just match them up 1-1

1 & 2 & 3 & 4
2 & 4 & 6 & 8
Etc.

1

2

1

Can you not think of it using only shapes? I can.
Squares where you put in a certain amount, take out the first of that amount. It's like a wave always getting bigger, but as the wave reaches infinity, the gap from the start is growing at a 1/10'th pace.

As they both grow to infinity, the gap beats it, because it becomes infinity - infinity, rather than 10 - 1?

Assuming a coefficient of friction of 0, it would indeed carry the previous momentum.

...

But what if they're numbered. If there's always more in than out, name a number that still remains in the vase after 2 hours have elapsed.

name of the number has nothing to do with anything real

it's not a 1 to 1 matching though- it's a 1-9 matching, for every 1 you take out you match that to the group of 10 you put in.

No dude, here's the simple reason you will never be left with no marbles in the vase... Everytime you fuck with the marbles, you put in more than you take out, so you're not actually taking any out, you're just putting more in, you might take out infinity marbles, but that means you're putting in an infinity of marbles ten times larger in, which leaves you with an infinity of marbles 9 times larger than the infinity you took out, still in the vase.

It's not about real marbles and vases, it's about math. Under the rules of the system that were established, what should be the case. Not whatever your monkey brain tells you about little pieces of glass.

am i wrong?

infinity times 10 is still infinity

> American education at work here

yo user, networking student here, working in my MCSA atm and planing on going into Cisco soon. can i ask you about your work?

If you're giving all the information, then there will be no marbles left after 2 hours.

I mean. Theoretically if you could move at an impossible speed. There is an infinite amount of marbles in the vase. Right?

if n is the iteration of steps you've taken, and we take out the marbles in the order that they were put into the vase- then on any given iteration, we've taken out all the marbes 0 through n. But we will always have at least marble n * 10 - n through marble n *10 still in the vase.

You assume that just because something holds with finite numbers that it holds in the limit to the infinite. This is a faulty assumption.

Except that infinity is irrelevant? You'll have a huge ass amount of marbles, but you'll still have a finite amount. Infinity shouldn't be entering the equation here

Yes but what you're telling me is that one infinity is larger than another.
I tried to show that that isn't very structured logic by showing two sets where one set of infinity numbers should be half of the size as another set of infinity numbers, and showing that they can match up. Because it scales up infinitely, it doesn't matter that one set is bigger than another in a finite cross section, because they are both equal in infinite space.

An infinity 9 times larger than the amount taken out. That's the most precise and mathematically correct answer there is.

Not my fault it's a shit puzzle.

Then name a number that's still left in vase. We've only put marbles in that have an integer n on them, so clearly there can only be integers left in the vase, so name one.

How can divide 1 in half an infinite amount of times. Right?
That's were infinity would come from

well no your wheeling is correct, but the last wheel will make the needle go to 2 since it's spinning in that direction

You're right. It's 2.

But we only put marbles with finite numbers on them into the vase, so only marbles with finite numbers could be left in the vase. So name one of them.

2?

Sure mate go for it, if you want the general idea of it, everybody that uses a computer and is not in your company is a fucking idiot and you're basically a computer janitor that goes around sorting all their shit out. We have so many stories about fucking dumbass clients.

If any one actually needs to be run through the math of the marbles in the vase thing, see this forum thread that goes through many different versions of this problem very explicitly.
forums.xkcd.com/viewtopic.php?t=45522

you got more like this, i thought it was fun.

But you can divide literally any number in half an infinite amount of times.

ok one sec, my math was wrong, on the nth step we have at least n + 1 through 10 * n still in the vase. So a number still in the vase is n + 1. So on 1st iteration, 2 is still in the vase. On 2nd iteration marble 3 is still in vase. And so on ad infinitum. So infinity + 1 is in the vase as we approach two hours but never reach it.

I'm English you fucking pleb and there are different levels of infinity.

Infinity is a concept not a number and infinity to the power 2 gives you an infinity, infinity times greater than the one you started with, if you can't comprehend this then don't fucking reply.

Yeah, I'm not saying we don't have an infinity here, I'm just saying that not all rules that work on purely finite numbers work when you bring infinity in. You can't assume that just because your logic holds for the finite that it will hold for the infinite, you have to prove it separately.

Ok let's say your adding 10 ten an infinite amount of times. But your also taking away 1 for every time you add 10.
(10-1)x infinity?

Idk why but something in me is telling me the answer is 9. No fucking idea why that makes sense

oh yeah whops.

it's called using induction. Look it up.

No, in this case, by 2 hours, we have reached it. And by 2 hours all balls have been removed because we've only put in balls with integers on them, and we've removed all integers. The result is actually different if they weren't numbered.
See:

But how can we not reach it if the time is still technically increasing?

You're dumb you can't answer it with a finite number because the number of marbles put into the vase before the two hour mark, discounting how long it takes to put marbles in a vase, is infinite, because you never stop putting marbles in.

Yes, I'm aware. But look up the axiom of choice. It's patently obvious that for any finite set you can choose an element for each, but to choose an element from every subset of an infinite set in the general case you have to invoke the axiom of choice. And in this marble problem, we don't merely approach infinity, at 2 hours, we reach it.

No, I've explained it enough times, go be dumb if you want but know you're wrong and stupid.

But we only put marbles with finite numbers on them into the vase, when did we put in all these marbles without finite numbers on them then?

The time isn't increasing, you're dumb.

Have you heard of the Dunning Kruger Effect? It's hilarious to me to see people with an 8th grade level of math be so hilariously over-confident about math.

Yeah, go ahead and be quiet.

t. centuries of mathematicians

Can someone explain why the simple answer: infinity. Is wrong?

Well, the time is increasing, but the rate the time is increasing at is halved?
To be fair, it is very hard to get your mind around sometimes.
I think the point is that there are infinite decimal places to go, so there's always a new 'closeness' two things can get without ever touching, mathematically...

No? Then what's it doing. Because its not standing still, and its certainly not moving backwards

thanks for that. axiom of choice I mean.

I now realize I was wrong since I was assuming an order in which the balls were removed, instead of using probability to determine on a ball to ball basis how likely it was to be removed at the end of infinite removals.

I have applied the science to reality by taking a bag of marbles and putting them in the vase for two hours as described and the total amount of marbles in the vase is 81. Problem solved.

Yes, there are different kinds of infinity, but it also matters how you get there. Which is why you can still sensibly take limits like lim{x->inf}(2x/x) and reasonably get an answer of 2 even though you're dividing an infinity by another infinity. In this case, we're adding all the positive integers to a vase, and then we're removing all of them from the vase.

I'm not saying you'd pull out a marble number infinity you dumb fuck lol you've put so many marbles in that you can no longer have finite numbers on each one, if you say you only put finite numbered marbles in the jar then here's what happens:

A. You run out of marbles
Or
B: You run out of space on the marbles to number them

Take speed. Report back in 2 hrs.

It's asking about the 'end', when you don't reach 2 hours unless you can comprehend going past a finite number of terms.

There is real life analogue, especially within time, I think..

These are mathematical marbles, we neither run out of marbles since you never run out of positive integers nor do we run out of space in which to write as we can always write smaller :)

Passing, increasing implies that it's getting bigger, which is not, it's always 2 hours, it passes.

So you're saying there's only one level of infinity?

You're right, I apologize for not using the correct terminology.
But also, fuck you, you knew exactly what I meant.

What does it all mean though? Besides being fun to think about.

>Besides being fun to think about.
That's what most mathematicians are in it for.

The "puzzle" is just a stupid example from a philosophy course. The trick is that you are putting in infinite marbles, and also removing infinite marbles. But obviously to say anything other than "It will have infinite marbles" is stupid because they are asking about the state of the vase after infinity steps (which will never happen by definition).

You can't subdivide time infinitely, Zeno's paradox proves that math is not real, stop masturbating with numbers.

Mental Masturbation

> This is confusing to me therefore it must be dumb, it couldn't be that I'm just ignorant and haven't actually spent the time to try to understand it

> (which will never happen by definition)
By definition, it does happen, after 2 hours.

I already said it will have infinite marbles, I'm arguing against someone who said there would be no marbles...

Thanks for backing me up lol

You would be correct in the original statement of the problem where they weren't numbered. But in the numbered case, there are no marbles left.

No I didn't, I thought you meant increasing, because you said increasing.

nah bro, I have a PhD. I fully understand the argument. Zeno's argument is that when you divide time in half forever, you'll find that you never actually reach the end. He makes the argument in a bunch of ways (an arrow coming at your face, or two chariots racing in opposite directions, etc).

His whole argument is "Time is not infinite, you can't cut it in half as much as you want". And it's true. Quantum mechanics proves that there is a "smallest" quantity of time. You don't actually end up with infinite marbles, because there is a physical limit to cutting time in half.

The example is straight out of a sophmore level philosophy course. If you treat it as mathematics, then yes you're taking "infinity-infinity" which, depending on your numbering scheme, literally means ever integer is a "correct answer". That's why it's stupid and Zeno is right, 2000 fucking years ago. Get it through your stupid head.

I make dank memes

Lol sorry my mistake, I didn't know I was arguing maths with a fucking philosopher, you know the thing about philosophy is nobody is ever right, it ponders the questions that "can't be answered" so if you're gonna argue with anything, I'll let you converse with a child. If you wanted a mathematically sound answer, you already got it. Goodbye, and good luck with your worthless degree.