Well Veeky Forums?

Well Veeky Forums?

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en.wikipedia.org/wiki/Cantor's_diagonal_argument
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None because you have to take the marbles out to remove the labels and you can't go back in time to do that

Thought its gonna be some derivations or functions limit:
Actually its just wrong written riddle that has nothing to do with math.
t{0, .5, .7, 1}? Or what are the t values?

10-1+10-2+10-3 = 24

24 marbles

Removing labels doesn't affect amount of marbles

24 marbles

You do the described procedure an infinite number of times before you reach 1. First at 0, then .5, then .75, then 0.875, and so on. At the nth step, you add the next 10 marbles and remove the nth marble.

>I watch Vsauce: The thread

Here it is:

>n is how many times you do the addition (the "at time 0, at time 0,5 at time 0,75 at time 0,875 is just mystification; *point* is you do the addition n times, where n must be chosen; no function can produce you n; you need to choose it, so to have a solution we must choose n).
>10n - n = x

n=0, x = 0
n=1, x = 9
n=100, x = 90
n=1000, x=900
n=10000, x=9000
n=inf, x = 9*inf (9 times infinity)

If you don't CHOOSE the n, only solution is "10n-n = x"

Problem solved. Consensus reached. Next problem.

I'm sorry if the statement was unclear, you're meant to repeat the procedure a countably infinite number of times. If you want me to say it more specifically here you go:

For each integer n greater than or equal to zero, we do the following procedure at the time [math] t = \sum_{k=0}^n (0.5)^k [/math]: add the marbles labeled 10n + 1 to 10n + 10 to the jar, and remove marble n+1 from the jar.

As you can see, there will be a countable infinite number of points in [0,1) in which marbles are add/removed from the jar. The question is how many marbles are in the jar at time t = 1.

Undetermined, there is nothing in the problem that logically determines what the state should be at t=1. All you know is what the jar looks like after each of infinitely many finite steps; you're missing a principle that tells you what it looks like after infinite steps. I could say 6 marbles and nobody can prove me wrong.

This shit is older than vsauce. Did he just do a video on it or something?

You didn't even read my post.

Tell me what N is and I can solve it.

If you don't tell me what N is then the solution, and the only possible solution is:

10n - n = x

Anyway. It's a solved problem. I won't respond to your messages anymore. Problem solved. Consensus reached. Next problem!

Why are you asserting N must be chosen. The statement of the problem says N equals infinity. If you're asserting that there are infinity many balls in the jar, that's fine.

Labels are only there for convenience, they change nothing.

There will be no marbles in the jar at [math]t=1[/math], because every marble will be removed from the jar at some time before then.

N = infinity
X = 9*infinity (9 times infinity)

1*infinity = line that is infinite length
2*infinity = plane that has infinite area
3*infinity = cube that has infinite volume
...

Ok, so if there are infinitely many marbles in the jar, can you name one? They are numbered after all.

>Tell me what N is and I can solve it.
10^200

Hmm, that is actually a very good question. I'll have to think about that.

If the marbles aren't labeled, at each step the net result is adding 9 marbles, so it's clear there must be infinitely many. Unlike in the first case, you can't be sure any particular marble is ever removed from the jar.

The infinite variable amount, minus 4.
There's no such thing as infinity.

The nth marble is removed at the nth steps. Eventually every marble is removed, so the answer is none.
Is this supposed to be a trick question?

Here is solution to the names of the marbles.
Expect I don't know how to formalize the path that you have to draw through the 9D cube.

I bet you guys don't know why pic related is wrong.

But that's not actually so wrong.
Just replace it so that the corners touching circle are connected by line, then you have a modern definition of pi.

okay, this is the correct answer:
it's literally impossible bullshit and its proven.
en.wikipedia.org/wiki/Cantor's_diagonal_argument
You only have [math]\aleph_0[/math] marbles, but you have to do this crap for [math]\aleph_1[/math] times.

That's nonsense, marbles are added or removed countably many times. Where does [math]\aleph_1[/math] come in?

it's a sum of countably infinite terms and you're adding a constant number of marbles in each term, so it's countably infinite. unless it's some trick question, in which case i'm far too tired to figure it out.

or i should say, it's a sum of a countably infinite number of terms.

there are two possible outcomes, that in a way amount to the same thing.
1. The time that it takes to put the marbles into the jar has a lower limit. At some point you will not have time to put any marbles into the jar anymore.
2. If you succeeded in placing an infinite amount of marbles in the jar, that is, if the placement of marbles in jar and taking away a marble from the jar took no time, then you end up with an infinite amount of marbles in the jar, AND and infinite amount of marbles taken out of the jar. In this case the putting of marbles into the jar and taking one out after very set, never ends. that action is going on forever.
infinite is not a number, so having one infinite set divide into two infinites like this is not impossible.

No, you're just extending finite results to the infinite. Every ball is removed regardless of whether they are labeled.

i put the times and marbles given in a ti-84
0, .5, .75 into L1
9, 18, 27 into L2

then ran ExpReg on those and got an r value of .999..., stored the equation into Y1 and so Y1 (1) gave me roughly 38

OI OP I KNOW YOU WERE AT THE H3 LECTURE. I KNOWW BITCH.

the prof is cool thou

>why
1) it isn't a limit because the perimeter is constant
2) even if the perimeter would vary, this would only give the upper limit

yeah, you're right

-1/12

Fuck you I was going to post this

>1) it isn't a limit because the perimeter is constant
That's what I thought, you have no idea why it's wrong.

The answer to OP problem is none is left. For any marble K, it will be removed at step number K. Conclusion, no marble is left.

That statement is not fundamentally different from saying "There exists an infinitely large set of countable objects. Count them one by one and never stop. Then say how many you have."
Instead of thinking of a jar that you're putting numbers in, think first that you have an infinite jar that you're taking them out from. The numbers already all exist, and it doesn't matter in which jar they are. At every step along the way in both cases, you'll have infinitely many left to go, but the only thing that matters is that you're going through all of them without skipping any.

If the jar has infinite marbles labeled 1-10 then how do I put 1-10 into the jar without taking it out first

The jar can hold infinite marbles, but it is empty at the beginning.

An infinite number of marbles, says so in the first sentence.
Whatever you do to the marbles after that is never gonna change that.

>but it is empty at the beginning.
Where is this stated?

>Suppose I have a table which can contain an infinite number of crayons, and I have an infinite number of crayons labeled 1, 2, 3, etc.
>At time t=0 I place crayon 1 on the table.
>At time t=0.5 I place crayon 2 on the table
>At time t=0.75 I place crayons 3 and 4 on the table
>I proceed in this fashion until time t=1. How many crayons are on the table at time t=1?

>Suppose now I remove the labels from the crayons. How many crayons are on the table at time t=1?

Do you see the problem? In order to achieve an answer you must make an assumption about the procedure of events and the functional model.

Lrn2clrlydefinetermsyouscmuck

your function in t=1 is not defined. boom.

It's an interesting sort of question, I think you'd basically have an infinite number of marbles, all labelled with "numbers higher than you can think of". The number of marbles is always increasing (9 per step), but the lowest number left is arbitrarily large.

And really that's why we don't have to think about it: this kind of arbitrary time compression doesn't exist in the real world. How could you pick out the marble to remove under all the others in half the time you did it last time?

>ask a mathematician
>just an infinite number of marbles
>
>ask a physicist
>[math] \displaystyle \sum_{n=0}^\infty 9 = 9\zeta(1) = -\frac{9}{2} [/math] marbles