>Roll a D20 an infinite number of times >Never roll a 1

>>47683615
theoretically its possible to only roll 8s

>>47683615
It's just a chance so, yes. But with each roll you're in danger in rolling a 1. I'm probably not the best person to say, I'm sure an anon can give a much more detailed explanation whether it's impossible or not.

>>47683626
>>47683659

That doesn't make sense.

>>47683615
Yes, but with each roll the chances of it happening continue to get lower. Someone will know the math; we have several resident mathfags who love to post about the mathematical mechanics of dice and probability.

>>47683685
why

>>47683691

Well, not really. The probability of rolling any number not a 1 is 95% consistently so long as the dice are assumed to be balanced and the rolls are truly random. The probability that trend continues is unlikely, but the probability of each individual roll never changes

>>47683615

>infinite
>never

Pick one.

It is a basic limit problem. As you keep rolling the dice, the chance that you don't roll a 1 gets smaller and smaller. The number infinitely approaches zero, but never actually reaches it. Meaning that it is theoretically possible, just not practical.

>>47683615
Improbable. But not impossible.

>>47683676
>>47683659
>>47683626
>>47683706
you see, OP said infinite. assuming a perfectly fair d20, in an infinite number of rolls, every number happens the same amount (1/20 of the time)

>>47683615
Yes, if you can control your rolls.

>>47683615
As the number of trials approaches infinity, the probability of not rolling a one at least once also approaches 0.

That being said, there is nothing useful you can draw from this, as it is impossible to roll a die an infinite number of times. Any finite number of times, however, has an extremely small chance to not roll a 1.

>>47683691
The presentation of this idea has always bothered me.
The possibility of rolling a 1 on a 20 cited die is always 5%.
The possibility of rolling a 1 twice in a row is less and so on.
No matter how many times you've rolled a one, if you roll the die there will be a 5% chance of getting a 1.
Just making that clear.

>>47683615
Possible but highly improbable.

>>47683691
>Yes, but with each roll the chances of it happening continue to get lower.

To explain the math here, think of it in terms of limits. The base chance of not rolling a 1 on a fair d20 is 0.95. The chance of not getting a 1 when you roll twice is (0.95)^2 or 0.9025.

Let n be the number of times you roll a fair d20. So the limit as n approaches infinity (roll it an infinite number of times) is (0.95)^n which approaches 0. It is a minuscule number that is so close to 0 you can say it is 0.

So possible but highly improbable.

>>47683767
>there is nothing useful you can draw from this

Let's say that physical reality persists in some infinite fashion. Does this mean that every possible animal will exist at some point?

>>47683615

>roll a d20 an infinite number of times
>is this theoretically possible

no

case closed

the part about rolling a 1 doesnt even come into the equation

>>47683745
>The number infinitely approaches zero, but never actually reaches it. Meaning that it is theoretically possible, just not practical.
Wrong, as the trials approach infinity, the limit also approaches 0. It is impossible to not roll a 1 during an infinite number of trials, as the probability is 0. It being "improbable" implies a finite number of trials.

>>47683783
There are many different kinds of infinity, anon. First we must define what every possible animal is: is it every possible species that would fall under our definition of animal? Is it any motile form of organic life? Is it any motile form of life at all? Is it every any any individual of any kind of life? Is it every and any possible state of that individual that may or may not exist at any time?

>>47683685
See
>>47683745
and
>>47683767
It like halving the distance between two points. Technically you never reach the second point, no matter how close you get. But that's theory not practical reality.

>>47683812
>Technically you never reach the second point, no matter how close you get. But that's theory not practical reality.
Close; you do arrive at the second point as soon as you reach the time required to arrive at it. You only approach that point while you are approaching that time.

>>47683805
>First we must define what every possible animal is:

>is it every possible species that would fall under our definition of animal?

I had something like this in mind.

>>47683615
No. You will roll exactly an infinite number of 1's.

>>47683805
>It is impossible to not roll a 1 during an infinite number of trials, as the probability is 0.
I agree with the other Anon. It approaches 0 but infinity never ends so while practically it's impossible, it never actually reaches the end and never actually reaches zero just like those pesky two points.

>>47683615
Surely you must eventually roll a 1.

If we assume a fair dice, the chance of not rolling a 1 is 0.95. Raise 0.95 to increasingly large powers (approaching infinity) and you'll find yourself quickly approaching 0% chance of it happening.

>>47683764
Shut the fuck up.

>>47683812
>It like halving the distance between two points.

Zeno's paradox. If I remember right, the solution is that the sum of all those infinite half-steps is 1. Infinite geometric series.

>>47683827
>Close; you do arrive at the second point as soon as you reach the time required to arrive at it. You only approach that point while you are approaching that time.
What are you talking about? You only halve the distance. No matter how small the distance it is, half the distance still remains.

In theory but not in any practical terms

>>47683863
There is no difference between 0.0 repeating and zero. If the probability is infinitely small then it IS zero.

>>47683900
Only if you halve the steps of time you are taking.

>>47683856
>No. You will roll exactly an infinite number of 1's.

>>47683626
Yes.

>>47683659
>theoretically its possible to only roll 8s

Somehow all of these are correct.
Infinity, ladies and gentlemen!

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>>47683939
>Somehow that's correct.

Is it safe to say that infinity is evil?

>>47683615
No it is not.

Rolling a 1 on a d20 is a 5% chance. If you roll an infinite number of times, then you will roll a 1. Now, whether it will actually be 5% of the time is debatable, but you will definitely roll at least one 1 in an infinite number of rolls.

>>47683932
Almost

>>47683900
Actually, that paradox falls apart when you factor in plank length.

>>47683972
What if the die had 2 sides that read 11 and no side that read 1?

>>476839>>47683932
Except that the probably was never 0.0 repeating instead it is 0.000000...01 where the zeros preceeding the 1 are infinite. Therfore, infinitely small, but still not zero.

>>47683937
Where are you deriving "the time required to arrive at it"?

>>47683615
Yeah

>>47683965
No, but it's a dirty word.

>>47683932
Something is not nothing, and there's always 19 other faces for it to land on. There's ALWAYS the chance for the one to not come up with every roll.

>>47683615
Fuck the stats approach. You can never reach infinity - you can always roll again, and you are going to roll until you roll a 1. Therefore, you are going to roll a one before you reach infinity. QED it is not possible to roll an infinite number of times without rolling a 1.

>>47683615
No.

Because you cannot roll a d20 an infinite number of times. You are mortal, and therefore have a finite lifespan, and thus a finite number of times you can roll a d20.

>>47683982
>falls apart when you factor in planck length
Well, what doesn't when you get there?
We're talkin' theory here.

>>47683997
One third is 0.3 repeating. Two thirds is 0.6 repeating. Three thirds is 0.9 repeating. Three thirds is also 1. What is the difference between 0.9 repeating and 1?

Infinity is infinity because there is no end to it. There is no ..01 because there can't be.

>>47683997

This is why we have limits in mathematics, because of stupid people like you.

>>47683982
You just move half a planck length forward

>>47684063
Also, it is recurring, not repeating... How's common core going kido?

>>47684004
From your speed; if you move x distance in t tine, than you will move x/2 distance in t/2 time, and x/4 in t/4, and x/8 in t/8, and so on, assuming no acceleration.

>>47684083
https://en.wikipedia.org/wiki/Repeating_decimal

>>47683685
>>47683740

The outcome of one roll does not influence the next

You can roll it an unlimited amount of times and only roll (2-20) , yes.
You cannot roll it an infinite amount of times and not roll a single one.
The reason behind this is, if something is done infinite times, every possible result will occur.
It can be done an unlimited amount of times in a row and only have a single result , becuase unlimited does not imply the trial is done infinite amounts, it just means there is no determined inner limit to amount of times you can roll a (2-20) In a row.

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>>47684083

>>47684072
And you move either 0 plank lengths forward or 1 plank length forward. A plank length is literally a physical limit as to how small a distance you have to move. Anything less and it is not movement. Also, theories like this are utterly dismissed as useless because it's just another "Has no impact on anything physical and is disproven by tapping two pencils together."

>>47684113
>The outcome of one roll does not influence the next

You say that, but what about quantum physics?

>>47684072
I.... have very mixed feelings about this post

>>47684063
>There is no ..01 because there can't be.
It's there.
It's waiting for us at the end of infinity.
3/3 equals 1 and not .9 repeating in the same way that Infinity divided by Infinity equals 1.

>>47683615
No. You cannot roll infinite times.

>>47684148
>You cannot roll infinite times.

but gods can

>>47684097
You assume much and know little.

>>47684124

This guy gets it. There is a difference between "an arbitrarily large number of times" and "an infinite number of times."

>>47683759
It's impossible to roll a d20 an infinite number of times in practice, everything we're discussing is purely theoretical and theoretically speaking it is possible that you will never roll a one. Just improbable to the point of impossibility.

>>47684142
>Infinity divided by Infinity equals 1
>being seriously so wrong
What are infinity cardinals for 200, Alex?

>>47684127
As surely as .5 is half of 1 and .25 is half of .5 there's a half for all things. You'll never move a half planck with that kind of motivation.

>>47684127
>Also, theories like this are utterly dismissed as useless because it's just another "Has no impact on anything physical and is disproven by tapping two pencils together
I like to call this the difference between something being true and something being effectively true. You don't reach the other point but you effectively do.

>>47684142
>at the end of infinity

Just... read that statement back to yourself.

>>47684132
Jesus Anon, can we not get that far into this?

>>47684181

I like this configuration.

OP is effectively a faggot, even if he hasn't actually sucked a cock yet.

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>>47684175
>What are infinity cardinals for 200, Alex?

>>47683893
Actually, the solution is that space and time are not infinitely divisible.

Even though it is true that the infinite half-steps of distance all add up to 1, and the half-steps of time approach zero, that still does not address the fact that the half-steps never actually REACH zero time to accomplish. Thus, you have an infinite number of steps to complete, all of which require a non-zero amount of time. Therefore, you can never reach your goal, as the time required is infinite -- no matter how much time you spend travelling, you still require just a *tiny* bit more to make that last step. And once you do, you find it wasn't actually the last step, and you still need a *tiny* bit more, etc. etc. literally ad infinitum.

The only way to terminate the series is if the remaining distance and/or time cannot be further divided, due to reaching an inherent minimum unit of reality, so you're forced to "round up" and finish. We don't know how big or small these minimum indivisible units of space and time are, but we can know that it must exist. At least assuming we're rejecting Zeno's conclusion that movement is in fact impossible and all that we perceive as such is simply an illusion.

>>47683615
>Is this theoretically possible?
Yes.


Probability (P, expressed as a decimal between 0 and 1) of getting at least one nat 1 on a fair d20, over the course of N rolls:

P = 1-(0.95^N).

As N approaches infinity, P approaches 1.

Take a relatively small arbitrary number, like 200, and put it in there, and you get about P= 0.99996.


So, it is theoretically possible, but I'm not putting any money on it.

>>47683615
No, because you can't roll a D20 an infinite number of times. Bad question. Ask a bad question, get a bunch of bad answers. Also you're making inherent assumptions about the nature of the die. It it had no 1 on any of its faces, then the answer is "yes, of course, you moron."

If you mean "what is the probability an event A with p=0.05 never happening over N trials as N approaches infinity?" then the answer is 0, so, no, you cannot never roll a 1. Mathematically this reduces to lim(0.95^N) as N->infinity which evaluates to 0.

Also Zeno's paradox holds water only if space and time are both infinitely divisible. This is not an assumption that can be reasonably tested, but Max Planck's theories claim that space is NOT infinitely divisible, undermining the assumptions behind Zeno's paradox and making it invalid.

>>47684158
How so? That is the definition of speed. Acceleration would not change the problem, so long as we knew the initial acceleration (and its rate of change, if any) as well as the initial velocity.

>>47684187
Just... ask yourself what you hoped to accomplish with that post.

>>47684195
>Jesus Anon, can we not get that far into this?
>Wheredoyouthinkyouare.jpg

>>47684247
It's only theoretically possible as long as you have a finite N. As soon as your N stops being finite, it is not theoretically possible.

Only if you can control enough factors to deterministically throw the die. In a similar vein, there is a robot that appears to be able to do it with a coin, but without testing it an infinite number of times its accuracy being 100% cannot be experimentally shown.

>>47684264
What if, in the process of repeatedly halving the distance between theoretical points, I pause for a cigarette?

>>47683900
Physically, you can't halve a Planck length.

>Is this theoretically possible?

No.

Also,
0.9... = 1
Achilles reaches the tortoise
Zeno's arrow is moving, he just didn't know about special relativity and frames of reference
The other twin is older due to multiple different inertial frames during his journey
Cooperate with the other prisoner if you don't know when the game ends, backstab him if you do
The cat is a macroscopic object so quantum effects aren't noticeable at that size, but it's true of small particles
There are no hidden variables, Einstein was wrong
Switch the goddamn door when Monty gives you the option

Also next time you should go to /sci/ if you need help with high school math and physics problems

>>47683615
No. If you roll a fair D20 infinite times, you will get a 1. The odds of not getting a 1 start at 19/20 at n=1, and becomes zero as n approaches infinity. It's possible to get no 1s in any given number (even if you were to roll it multiple googolplexes of times or whatever arbitrarily large number you prefer), but you will always get an even number of each outcome if you roll infinite times.

>>47684330
Yes, that's been brought up.
The post you are responding to was in response to an Anon who was bringing in time to arrive for some reason.

>>47684236
He's got you there anon

>>47684316
memes

>>47683615
Fuck your metal dice. You're not infinitely rolling that on MY table.

>>47684333
>0.9... = 1
No.
3 times 0.3... = 1

>Switch the goddamn door when Monty gives you the option
This is not always right either.

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>>47684333
>The cat is a macroscopic object so quantum effects aren't noticeable at that size
Excuse you.

>>47684392
Is that somehow an established meme?
Or are you just broken?

>>47684403
https://en.wikipedia.org/wiki/0.999...

>>47684417
>not knowing that memes are the base unit of all reality
Get back to me when you finish memetics 101, slugger.

>>47683615
Looks like the answer to this question is no. But what about rolling an infinite number of dice an infinite number of times? Would any of those infinite dice never roll a one?

>>47684161
>There is a difference between "an arbitrarily large number of times" and "an infinite number of times."
This. Infinity does not just mean "really really large." It means forever. You cannot have a positive probability that never occurs in infinity because it NEVER stops checking. With a finite chance, you can get to the end and find yourself lucky. The whole POINT of infinity is that it doesn't HAVE an end.

This is also why limits taken to infinity have coherent answers. The limit of the summation of 1/(2^N), where N=1 and goes to infinity is equal to 2. Not alllllllllmost 2, or 1.99999....999998, but literally 2. That's because when it goes to infinity, it goes *all the way* to infinity.

>>47684423
See
>>47684181

>>47684450
no you fucking ape

>>47684240
You are right, it is easier than that. That is Aristotle's solution with the assumption of infinitely divisible space and time being wrong as you said. Apparently the infinite geometric series is an exhaustive solution by Archimedes made with the assumption being right.

>>47684444
But how is the word "memes" a fair answer to the question?
>inb4 because memes

>>47684457
The way I explain this to people is the infinite hotel metaphor.

If a hotel has infinite rooms, and infinite guests in all those rooms, but someone show's up asking for a room how does the manager accommodate him?

>>47684457
This; people always say "the limit as x approaches n", rather than "the limit of x at n"

>>47683615

If we're talking about some large finite number, there's a non-zero probability of never rolling a 1. If we're talking about infinity, you should probably use a limit treatment.

lim(x->infinity) (0.95)^x = 0

Infinity and limits are already math theory. Proposing to roll a dice an infinite number of times is already a thought experiment. Asking if it's "theoretically" possible is both redundant and misleading, since it tricks poor, innocent anons into answering the question "if you rolled a dice a large finite number of times, is it theoretically possible to never roll a 1?"

>>47684489
Because it's a nonsensical question; pausing for a cig is utterly irrelevant to the situation at hand.

>>47684450
No, because the odds of any particular die failing to roll a 1 are zero. Same reason you'll get 0 results of 34 or Zebra unless you're using cheeky dice: Infinite guarantees all the physically possible results, but it doesn't generate new ones.

>>47684486
The geometric series is just a fancier way of proving Aristotle's solution. It still relies on the assumption of infinite divisibility, and an infinite number of steps.

By definition, an infinite series of steps can NEVER be completed. Even if they do eventually add up to the whole, it's a moot point because you will never, ever, ever, reach that "eventually".

>>47684510
It affects arrival time. Which was brought in for some damn reason as if it were a constant.

>>47683615

>theoretically possible?

Philosophically possible, because mathematics and probability.

Theoretically impossible, because of thermodynamics and statistical mechanics.

>>47684546
Stopping for a cig would change the velocity, which makes it irrelevant.

Speed is literally defined as distance/time, and if we know this distance we need to travel, and we measure the time it took us to travel the distance we have already gone, we can know the time it will take to get to our destination. Travel time IS constant, assuming velocity does not change. It is intrinsically linked to how far we must go, and the rate at which we displacing ourselves.

>>47684541
You will if each successive step is completed faster, up to infinitely fast.

>>47683615
Yes. Simply draw a 2 in front of the 1 to make it 21 instead.

>this thread
yall niggas need some bald science man.
https://www.youtube.com/watch?v=ffUnNaQTfZE
https://www.youtube.com/watch?v=SrU9YDoXE88

>>47684547
I guess the appropriate answer is what theory you're using.

Math theory for treating infinity (at the high school calculus level) says no. There's might be other ways to treat infinity that will say yes? Either way it has very little bearing on the practical action of rolling dice and getting fumbles.

>>47684596
>up to infinitely fast.
There's you're problem. You can never get "up to" infinity (or "down to" an infinitely small fraction, in this case). That's the very definition of infinity -- no matter how far you've gone, there's still farther to go.

The geometric series works as a mathematical proof, but mathematical proofs and physical realities are two different things. In math, you can skip over the whole issue of actually resolving an infinite number of steps. But in reality, it is by definition impossible to reach infinity by iteration.

>>47683615

>>Roll a D20 an infinite number of times
>>Never roll a 1

>Is this theoretically possible?

No, because you could never count all the rolls.
Never rolling a 1 requires all rolls to be countable.

>>47684583
But, you don't arrive at the second point just because the time you expected to arrive at it has passed.

>>47684506
On the other hand, if approached as a matter of set theory rather than a limit problem, it is possible to have an infinite series of non-1 rolls. The probability of a streak of n non-1 rolls is 0.95^n, but no matter how big your n, the probability of your n+1th roll also being non-1 is still the same as always: 0.95. Since the probability of not rolling a 1 on the next roll is always non-zero, there is no non-1 streak of length n such that you cannot propose a longer streak of n+1.

Therefore, the set of all possible non-1 streak lengths is infinite, and thus an infinite series of rolls can in fact possibly consiste entirely of non-1 results.

>>47684700
You can however have a countably infinite series of rolls consisting entirely of non-1 results; see >>47684797.

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>>47684797
>set theory
nice meme

>>47684127
>And you move either 0 plank lengths forward or 1 plank length forward.
Pretty sure we're talking about maths here, anon. Maths doesn't give a fuck about reality. We just frequently use maths as the basis for most of our science. They aren't the same

>>47684700
There are countable and non countable infinities, anon.

>>47684870
Speaking of, why is math so damn good at describing natural phenomena?

>>47684625
I was just about to post this when I was done scrolling through

>>47684925
Because observed natural phenomena that rely on only a few factors, or even out statistically to a few factors, end up being relatively easy mathematical functions.

The more factors you involve, the more complex your math needs to be.
>In b4 muh epicycles

>>47684403
It's right 2/3rds of the time, better than the 1/3rd odd that the first one you picked was the right one.

>>47683615
It's not theoretically possible, because it's not theoretically possible to roll a D20 an infinite number of times.

If you roll a D20 an arbitrarily large number of times, yes, it is possible to never roll a 1. But as the number of rolls approaches infinity, the probability of never rolling a 1 approaches 0. Since the number of rolls can never reach infinity, the probability of never rolling a 1 never quite reaches 0.

>>47684877
>>47684817

Infinity actually is not countable.
There is a kind of infinity called "countable" but it is a bad name, because you of course cannot count to infinity.
"Listable" is a better word, since you can list numbers in that infinity.

>>47685085
It's "countable" because that particular infinity is in one-to-one correspondence with the natural numbers, which in themselves are a countable infinity by definition. They're "countable" in that, in any arbitrary interval, you can count one step at a time and eventually reach the end at some arbitrary time.

This is opposed to uncountable infinities in which it is impossible to put that infinity, or any subset or interval of it, into one to one correspondence with the set of natural numbers.

>>47685002
I don't think so.

Obviously, no, the sentence "roll a die infinite times" is pure nonsense. The second bit is irrelevant.

>>47685485
>Obviously, no, the sentence "roll a die infinite times" is pure nonsense.
You want to know how I know you'll never be a mathematician?

>>47683615
Almost impossible.

>>47683939
Infinity is shit. They changed the scale.

I seriously hope most people here are trolling.

The OP said infinite which means that every single possibility would occur.

Just like how if you had an infinite number of monkeys with typewriters they would eventually write Hamlet.

>>47685743
>they would eventually write Hamlet

Also Hamtel. It'd be exactly like Hamlet, but every instance of the word Hamlet would be replaced with Hamtel.

>>47685743
An infinite number of monkeys would instantly write every permutation of letters possible with the keys on the typewriter. There's nothing eventual about it.

>>47685698
Never work for scale.

>>47683615
Yes, this is possible. Roll 1, there's a 19/20 chance that you won't get a 1. Roll 2, there's a 19/20 chance that you won't get a 1. Roll 918972381763, there's still a 19/20 chance that you won't get a 1. Odds are extremely slim that you would avoid getting a 1 for that many rolls, but it's theoretically possible.
>>47683691
This is incorrect. Your odds of rolling a 1 are always 1/20 assuming a perfectly fair die. There is no law of averages. If you have 10 children who are girls, you are not "due" for a boy, odds are still 1:2

>>47685743
>>47685790
>>47685810
https://libraryofbabel.info/

The better question is, as X approaches infinity, does pimping become easier?

Probability of n dicerolls without rolling a 1
P(n)=0.95^n

Want to prove that ∀n∈N: P(n) > 0

For n=1: 0.95 > 0;
For n+1: 0.95*P(n)

Since ∀a,b>0: a*b>0 and P(1)>0, P(n)>0

No matter how many dicerolls, the probability of never rolling a 1 stays >0, therefore it is possible to roll a die an infinite amount of times without rolling a 1

>>47684113
That has nothing to do with it.
Infinite chances and "never getting a non-zero probability outcome" are mutually exclusive.

Basic stats. No quantum/metaphysical/heart-of-the-cards bullshit needed.

>>47683615
The math on that is weird, and basically eventually becomes the question of "is .9999999~ equal to 1" problem. The long and short of the answer is yes .99999~ is indeed equal to 1, it's just after such a near infinity long sequence of nines that it eventually reaches one.

Similarly, the answer is not that you can avoid rolling a one, it's that it WILL roll a one, but the number of rolls it would take in this scenario to do so is so great that it's final number is both irrelevant and classified as a near infinite number.

So basically, no for the literal answer, but yes for the practical answer.

>>47685834

Scroll up. Once we throw the notion of "infinite" into the mix, shit gets weird.

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>>47685954
Are you posting in Klingon?

>>47683615
The odds are infinitesimal but aren't zero.

>>47685966
When we say infinite, don't we just mean to take a snapshot at any given point and see if you can still roll a 1? The odds don't change, they're always 1 in 20. If we look at a graph, the probability of rolling a 1 by trial X is just an asymptote, right? It never becomes an absolute, but it approaches one.

>>47686046
We're asking if it's possible to never roll a one, which is 19 in 20, but that's a minor detail.

The actual thing is that we're not asking about any extremely large number of rolls, or the nth roll. We're talking about limits approaching infinity. You're right that the p(thing) asymptotically approaches 0. We're now taking the limit of the p(thing) function as it approaches infinity. In this treatment of infinity, the limit as x->infinity = 0. This is an entirely different ballgame from what you can graph or think about. IIRC, mathematicians were originally pretty suspicious of limits at first because this seemed like a weird, half-assed way to go about things.

It's ultimately an obnoxious math question from obnoxious math people, and not one that has any bearing on actual dice or actual rolls.

>>47686179
>what you can graph or think about
sorry, I misphrased this. You can think about it perfectly fine. It's just a different way of thinking about math and numbers (or the lackthereof).

>>47686179
w/e I almost failed Calc anyways. I'll let you guys talk about probability and shit.

What's your favorite dumb thing about infinity?

Mine is how there can be larger and smaller infinities

>>47686229
I like that infinities have cute, pointy ears.

>>47686280
That's elves, anon.
You're thinking of elves.

>>47686280
That's elves lad.

>>47686014
Yes they are.
see>>47685743

>>47683615
Only if the die is weighted. Peobability is defined as the amount of times it occurs over infinite trials so a fair die rolled an infinite number of times will roll a one exactly 5% of the time.

>>47686349
>>47686388
w-well, I like that infinities have strong, sturdy trunks to support their weight.

>>47683615
Short answer, yes
Long answer is long

First, let us define a set which contains all possible infinite series which, for each element, contains a number ranging from 1 to 20 as set A. Any experiment for which we would roll a twenty sided dice an infinite number of times, if we were to list out the result of any individual die roll in order, would produce an infinite series which, for each element, contains a number ranging from 1 to 20 which we can call series q.

Any series q that can be produced must necessarily be a member of set A. With that, we can deduce that some subset of set A contains all possible series q. This subset of set A must be the sample space for events resulting from any experiment for which we would roll a twenty sided dice an infinite number of times and list the rusult of any individual die roll in order. Any event that is a member of a sample set for an experiment must necessarily have a non-zero probability of occuring or else it would not be in the sample set. This means that if an event is in the sample space, it must be possible.

Since series q is constructed such that a possible series q is an infinite series which, for each element, contains a number ranging from 1 to 20. A set of all possible series q is a set which contains all possible infinite series which, for each element, contains a number ranging from 1 to 20. The constructed set of all possible series q is the same as the defined set A. This means that all possible member of set A is some series q.

>>47686539
Let us construct an infinite series in which every element is 20 (lucky fucker). This series does not contain the number 1. This series is an infinite series which, for each element, contains a number ranging from 1 to 20. This series of 20s is a member of set A. As a member of set A, the series of 20s is a possible series q. As a possible series q, the series of 20s is an event in the sample space of and can be generated by an experiment for which we would roll a twenty sided dice an infinite number of times.

Therefore, it is possible to roll a twenty sided die an infinite number of times and not roll a 1.

Q.E.D.

>>47684333
>Switch the goddamn door when Monty gives you the option

What if I wanted a goat, fag?

>>47684333
>macro objects aren't effected by quantum fucker.

What is a vacuum meta-instability event, anon? Or quantum fucking tunneling?

>>47686604
>quantum fucking tunneling
a thing that doesn't happen to macro objects.

>vacuum meta-instability event
I've heard of vacuum metastability events. what the fuck's an instability event?

>>47683615
No. Simple and clear.

Every roll has a 5% chance of rolling one. You have a 95% chance of not rolling one on 1 roll, 92% of no 1s in 2 rolls, and the number goes down. With any finite number of rolls, there is always at least a small possibility of not rolling a 1.

But we're dealing with infinites here. X number divided by infinite IS zero. Infinite is not a number, it's a concept. The same way you can have a hotel full with infinite rooms and infinite guests and STILL can fit an infinite number of new people in it, infinites don't follow common logic very well because they are not just "big numbers".

>>47683615
No. The limit of 1/20 * 1/20 ...-> inf = zero. That is, zero percent chance. Since it converges, this series is well-defined and can be stated that the probability of never rolling the x-face of any n-sided die is always zero as the number of rolls approaches infinity.

>>47687126
By the way, if you want proof of what I said,

1/20 * 1/20, infinitely many times is equal to:

1/20 ** inf (one twentieth to the infinity power). Check what Wolfram Alpha has to say:

http://www.wolframalpha.com/input/?i=1%2F20+**+inf

It's zero. The chance to not roll any face is zero.

>>47683615
Out of all the possible combinations that could come out of rolling a dice an infinite number of times, every result being 20 is one of them.

>>47683615
Yes.

Any given roll has a 19/20 chance to not roll a 1.
The probability of a sequence of n rolls not rolling a number is (19/20)^n.
Since we only care about not rolling a 1 on each roll, it's possible. The likelihood of that sequence is infinitely small, but that has no effect on each roll.

>>47687601
>The likelihood of that sequence is infinitely small, but that has no effect on each roll.
You're using some non-rigorous language here which weasels the incorrect conclusion using the correct starting information. It's true that rolling fair dice is independent probability, however, consider the sequence of probabilities that a 1 does occur:

1/20 * 1/20 * 1/20 * 1/20 * 1/20... = 1/20^inf = 1/inf

1/inf is well-defined as zero. Therefore the probability to NOT see a 1 (or any given face) is zero.

The reason independent probability multiplies the chances together is that there is a stipulation of never rolling a given face but rolling a fair die infinitely many times. So in order to calculate that probability, you must calculate the chance that a 1 never appears in an infinite set of d20 results. Think of it like:

The universe where you flip two heads on two fair coins is: 1/2 * 1/2 = 1/4
The universe where you flip three heads on three fair coins: 1/2 * 1/2 * 1/2 = 1/16

So while each does not affect the other, as they are not dependent on one another, the universe itself (or SET of those results) IS affected, as there's these possible universes for the first example:
HH, HT, TH, TT

And we want HH, so the chance is equally 1/4.

The same occurs no matter how many n-faced coins (dice) you roll, even infinitely many. The set (or universe) of infinite d20s can never fail to contain ANY of its possible faces, or it wouldn't be present on the d20 in the first place (e.g. you cannot roll 0 or 21 no matter how many times you roll).

Don't take my word for it, do the math yourself. 1/20^inf = 0% chance.

>>47688172
Oh in case you were wondering, the chance to see any given face is:

1 - (1/20 * 1/20 * 1/20...)
= 1 - (1/20^inf)
= 1 - (1/inf)
= 1 - 0
= 1 (or 100% chance)

That is, all results MUST occur.

>>47683615
no

Sure, just paint a 2 in front of the 1

>>47684275
anon1 pointed out a fallacy, anon2

>>47684403
wrong

>>47685335
you don't have to think so

It is possible to a certain extent. At some point the theory of truly large numbers kicks in and states that since the probability is so low, it actually is zero. So for a while it is possible, but once the number of rolls becomes large enough, the chance is so low that in physics it is correct to say that it is impossible.

>>47685988
first chapter of any discrete math textbook, senpai

>>47684403
.99... x 10 = 9.9999....
9.999.. - .99.. = 9 = 9 x .99..
.99.. = 1

>>47685954
Better check yoself before you shrek yoself:
>>47687126
>>47687164
>>47688172
>>47688205

>>47685954
This is what happens when you never learn to turn word problems into math. Here is what is ACTUALLY happening, (taken from http://forums.xkcd.com/viewtopic.php?t=17142)

If I roll a D20 (or any other die) an infinite amount of times, what is the probability of a 1 (or any other given number) showing up at some point?

I. 1 roll - 1/20 (generally speaking: 1/x)
II. 1,000,000,000,000,000 rolls - something terribly close to 100% (assuming we really roll a D20 or some other regular gaming die and not a D1000000000000000 or something similarly crazy)

So if I roll infinitely, is the probability still something like
a) "~100%" or is it
b) exactly 100%?

It's b) exactly 100%. It's just taking a limit.

The probability of getting at least one 1 in n rolls of a d20 is:

1 - (19/20)^n

Take the limit as n goes to infinity, you get 1 - 0 = 1, or exactly 100%.

See: >>47688205

More generally, if s is dice-sides, and g is wanted-side:
((s - g)/s)^n

Therefore as you roll it infinitely many times, the P of any given g = 1. Or 100%.

>>47683685
Because you are trying to fit a counter-intuitive, highly complex thought into the trappings of your simplistic, intuitive, misinterpretation of logic.

You are also creating a disconnect between reality and a thought-game, which no serious mathematician would ever do, because you literally have to ignore facts for it to function. Only fucking autists on the internet insist this is even worth thinking about.

So here is your correct answer:

A probability of something is not a guarantee of something occurring.

With infinite time and infinite trials, it is almost surely going to happen. We say almost surely for two reasons.

1) Given infinite time and trials, all possibilties will occur. If you roll a d20 infinite times, any and all possible results of such a roll will occur.

HOWEVER

2) There is no such thing as infinite time or infinite trials. The probability of a d20 being rolled an infinite number of times is absolutely zero, beyond a shadow of a doubt. There cannot exist an arrangement of our universe in which there is not a limit to the number of rolls that a d20 can experience. You cannot remove this factor from the equation simply because you want to.

So, if you roll a d20 an infinite number of times, you will get all possible results of that roll, but you can't roll a d20 an infinite number of times, meaning that there is non-zero possibility that you will never see a 1. Both of these facts exist simultaneously, and do not cancel each other out.

>>47683691
>>47683615
it is the same chance as randomly picking a SPECIFIC number from the amount of all numbers that exist (which is infinite). the chance to roll everything else than a 1 on a d20 is 0.95

therefore on an infinite amount of rolls , the chance would be calculated 0.95^infinity, => 0.00000...(infinite amounts of 0's)...0001

it is still possible , because it is only ALMOST impossible

>>47688637
Wow. Way to nail it to the wall and point at it.

>>47688295
>so low that in physics it is correct to say that it is impossible.
It may be correct, but it's wrong. A chance "so low it is said be zero" is still NOT zero. We just say it is to make it easier on ourselves.

>>47683615
Ask an mtg judge about Four Horsemen

>>47688347
>9 = 9 x .99..
Can you show your work, here?
Wouldn't it be:
9 x 0.999... = 8.999...9991?

>>47683691
>Yes, but with each roll the chances of it happening continue to get lower.
Well no. Every subsequent roll will still have 1/20 chance to roll a 1.
It's just that with every 1 you roll, you are are entering the realm of being more and more improbable.

I.e. if you rolled two 1s in a row, you have had 1/400 chance of it having happened (but it already did and you're living in that 1/400 chance).
Three 1s, it's 1/8000 but it's still already happened and you're living in it.
Four - 1/160000; five 1/3200000; six 1/64000000; seven 1/1280000000; eight 1/25600000000 and that's playing against odds 3.5 times the size of humanity.

>>47683783
Yes, because it means every conceivable configuration of matter will exist not merely at some point, but an infinite number of times.

>>47688996
grade A troll logic here

1/3=0.33333....3
3x0.333333....3=0.9999999.....9
3x 1/3 = 3/3 = 1
0.99999999....9= 1
9x0.999999...9 =9

>>47683805
>It is impossible to not roll a 1 during an infinite number of trials, as the probability is 0.

I'm not sure this is relevant. The probability of selecting any given real number from a continuous interval is exactly 0, and I'm pretty sure it's for the same reason, but if you do that very selection you're guaranteed to get a zero-probability event.

>>47684403
>This is not always right either.
Yes it is.
It's very easy to see if you look at it right.

View it as getting to select ONE door or TWO other doors.
You know that one of the two other doors has a goat amongst them.
But the odds of car being behind 1 door is 1/3 while the sum odds of it being behind one of two other doors is 2/3.

>>47688996
Being that multiplication is repeated addition. So (2x3)-2 = (2+2+2)-2 = 2+2 = 2x2

I may have made some slip because it's late and I was trying to write the proof from memory, but im pretty sure that's how it goes. As I recall it there are a few better proofs, but those are a great deal more complex.

>>47683615
I mean law of large numbers. It's theoretically possible, in the same way it's theoretically possible for a monkey to sit down at a keyboard, type away blindly for a couple of days, and end up with the complete works of Shakespeare; there's nothing physically preventing the monkey from pressing the keys in the correct order so it's theoretically possible, but the probability is so infinitesimally small that we can say with a good degree of certainty that it will never happen.

>>47689081
Theoretically possible is all OP wants.

>>47684486
Also I'm pretty sure that 1/2 is a magic number for the geometric series and it doesn't solve shit anymore if the fraction in question is, say, 5/7.

>>47684492
The hotel has infinite rooms. Those infinitely rooms are full of infinite guests.

The presumed logical problem assumes the rooms are all occupied and that no room is ever without a guest, however this new person seeking a room now qualifies as a guest as he is seeking a room. Ergo he is one of infinite guests, therefore there must be a room even if there is no vacancy.

I feel like people are getting confused between "roll a d20 lots, and take infinitely many tries" and "roll a d20 infinitely many times."

The monkey and keyboard thing isn't a good parallel. It's not a matter of persistence and every configuration being possible, because the idea of a configuration doesn't make much sense when talking about infinitely many anything. The people taking the limit approach are in the right here, if you roll infinitely many dice it is impossible for a 1 to not come up somewhere.

>>47683615
No, the d20 will break eventually and you'll no longer be able to roll it.

>>47688241
>anon1 pointed out a fallacy, anon2
No.
Here's a lesson in applied reasoning.

Anon1, >>47684275, was responding to a post that mentioned the one at the end of a string of zeros infinitely long.
When responding to a post that is talking about the end of infinity, you can be safely assume that the person you're addressing either:
A. Doesn't understand what infinity is and is ignorantly posting about it anyway
B. They are attempting to make a point and are actually aware of the irony of commenting about the end of infinity.

If A is correct, then they are likely too ignorant and stupid to realize their error by simply rereading their own post and Anon1's response is pointless.
If B is correct, then they're fully aware of the contradiction and therefore Anon1 asking them to reread their post is pointless.

Understand now?

>>47689180
Bah, linked Anon2 not Anon1.

>>47689145
Another solution is to move all the guests in each room to the next room over. Room 1 is now vacant, and you don't have any problems because you have an infinite number of rooms.

You can also create an infinite number of vacant rooms by moving everyone such that only even numbered rooms are occupied, but I don't remember offhand the algorithm for this.

>>47689045
See
>>47684403
>>0.9... = 1
>No.
>3 times 0.3... = 1

>>47689078
I get where you were going now.
But there is still a difference between "three thirds" and "0.999...".
Just not an effective one.

>>47683615

No, it's possible for the die to never come up 1, but it's impossible to roll a die an infinite number of times.

Either the die's structural integrity would be compromised from repeated rolls, or assuming a die impervious to deterioration the universe would end before the die was cast an infinite number of times.

>>47689296
The similarity of 3/3 and .99.. is honestly not the most interesting imo, look up why it's impossible to tune a piano on minute physics. It involves fractions being not quite 1.

>>47689076
>It's very easy to see if you look at it right.
>"From a certain point of view"
Slow your roll, Obi-wan.

>View it as getting to select ONE door or TWO other doors.
>But the odds of car being behind 1 door is 1/3 while the sum odds of it being behind one of two other doors is 2/3.
No matter how many times you pick a door or roll a die, the percentage stays the same.
No matter which door you pick of the three, the one you first picked, or either of the other two, there is a 1 third chance it is the winner.
Unless Monty lets you open both the other doors, the chances remain equal.

>>47689386
>Unless Monty lets you open both the other doors, the chances remain equal.

When you select your first door, you set down the 1/3 chance of car.

It's 2/3 chance that the car is behind one of the other two doors.
He shows you which one of them doesn't have a car, so that door's 1/3 chance of car transfers to the other door in the pair.

While your original door still has the 1/3 chance which doesn't change.

>>47689386
Three doors ABC. Car has 1/3 chance of being behind door A, 1/3 chance of being behind door B and 1/3 chance of being behind door C.

We name the door you select as door A and the other two as B and C.
From there we have 3 possibilities:

1/3: car is behind door A. Switching is loosing.
1/3: car is behind door B. The guy opens door C. Switching is winning.
1/3: car is behind door C. The guy opens door B. Switching is winning.

>>47688284
See
>>47689430
There's always going to be a 2/3 chance you have the wrong door, whether you keep it or switch it.

>>47689430
>While your original door still has the 1/3 chance which doesn't change.
No. The original choice had a 1/3 chance of being right.
The moment one door is eliminated, each door has an equal chance.
Whether you keep it or change it, that choice has a better chance of being right than your first choice did. But now, both choices are equal.

>>47689468
But you don't get the car if you know if switching is more likely to end well.
You could switch twice and choosing the first door you picked would be better odds than the second one, when nothing changed.
Your choice is not switch or don't.
Your choice is one of three doors, 1/3.

>>47683615
Yes as long as there is a non zero chance of rolling anything but a 1 it is possible, and as each new dice roll is in no way influenced by the previous dice roll this means you always have a 95% chance not to roll 1.

The fact this is most likely to be physically impossible to do does not mean it is theoretically impossible to do.

>>47683615
That depends if all your assumptions are true or not

1) Is there such a thing as true randomness, or are we just assigning randomness to things that have a predetermined result that we can't predict due to a lack of information or knowledge on our part.
2) Does infinity actually exist or is this merely a mathematical construct that does not actually exist.
3) If the concept of infinity actually exist does it exist in a state that would also permit a physical object to be rolled. For example just because it turns out PI is truly infinite doesn't mean it can roll a D20.
4) Can there exist a D20 that would be able to survive being rolled infinitely, or more accurately can this experiment continue after the heat death of our universe aka ignore entropy.
5) Do your experiments require an observer to confirm the results, and if yes is it possible for this/these observers to be able to observe an infinite amount of rolling.
6) Does the nature of infinity also allow for this experiment to be performed an infinite number of times which would be a required for success.

If all these assumptions (and others I didn't think about) are true than it is possible.

>>47683759
>>47683691

But every separate roll is still it's own roll. The chance of rolling a 1 does not go up so that when you're making roll X, you're guaranteed to get a 1.

You still have 19/20 chance of getting something else. Are the odds of it happening an infinite times in a row high? No, they're cosmically small, but they're not absolute 0 either.

You're not guaranteed to get a 1 by rolling 20 dice just because each have a 1/20 chance. They're not connected, they're still individual dice.

Same with rolling a million dice, or infinity dice.
Is the chance of getting at least one 1 if you roll 20 dice higher than if you just roll one dice? Yes. But the 20th dice has just as much chance as rolling a 1 as the first one, or the single one.

Fractions and probabilities are not like water you keep pouring into a bucket and when it's full, it goes ding, 1.

They're like throwing balls through a hoop. No throw is a guaranteed hit or miss as long as you're not out of range.

>>47683615
Technically the answer is yes though I'm pretty sure mathematically it is not

>>47683615
Depends on what assumptions you make, but i would say no, because the universe will end before your infiniteth roll

>>47690119
If the universe ends before he rolls a 1, you can say he won.

>>47690139
But then he didn't really roll an infinite number of times.

He beat the universe, but he didn't beat his own game.

Lets MATH with REALISM

Basic presumptions:
>OP still maintains regular lifestyle outside of rolling the die. Lets say that it leaves him 6 hours of dedicated dicerolling per day.
>Rolling a die takes 5 seconds
>Lets say he has 60 years left in his life.

He has 21915 days (incl. leap years).
Every day is 4320 rolls.
This is a total of rolls 94672800 over OP's leftover life.
So it means that he's batting for 0,95^94672800 odds.

Wolfram Alpha gives me ~2x10^-2108969.
Yeah that's
0,000000.......(TWO MILLION ZEROES plus change)....000002
Pretty long shot.

>>47690202
while that's not wrong, the question pertains to rolling it an infinite number of times, and "functionally infinite" is kinda messy when we're just talking about a human's lifespan.

That being said you could roll a dice an infinite number of times and never roll a 1. While the chance of not rolling a 1 grows closer and closer to 0% it will never actually reach 0%

>>47690202
Pretty long shot is as far from impossible as 10^10^10^10^10^10 is from infinity

>>47683805
Wrong, it will never be exactly zero. Just really, infantismally small. (loads of zero's before you get to numbers) anything else is just computational errors/"idontknowwhatthewordisinenglish" afrondingsfouten(dutch)

>>47690240
Yeah I know, I just math for funsies.

>>47690272
I can't besmirch math for funsies so you have me there

>>47689052
>but if you do that very selection you're guaranteed to get a zero-probability event.
Good point, except for one thing; any "real number" cannot be described exactly without rounding; you cannot randomly select a real number, as it is impossible to describe one.

>randomly select a real number, not necessarily rational, from between 0 to 1
>first digit is 5
>second is 5
>third is 5
>fourth is 5
>5
>5
>5
>5
>...
>1
>5
>5
>5
>...
>...
>...
>...
>0
And so on.
Any real number requires a countably infinite number of digits to describe, and if you cheat my cutting it off after, say, the tenth digit, you're excluding all real numbers which differ in the 11th, 12th, 13th, and so on digits from your selection pool.

>>47690268
Close; just as we say that the limit as x approaches n approaches y, until the limit IS y when x is at n, so too can we say that the limit AT infinity is something, it just so happens that you can't graph something at infinity.

>>47683615
Define "infinite number".

>>47690240
>That being said you could roll a dice an infinite number of times and never roll a 1.
The whole point is that you *can't* roll a die infinite times. The whole point of infinity is that it's outside the realm of physical possibility. You can, however, mathematically solve the equation for n=infinity, in which case you get the result of 0.

>>47684127
>A plank length is literally a physical limit as to how small a distance you have to move. Anything less and it is not movement.

A plank's length is the physical limit for how small a movement can be MEASURED. Not for how small a movement can BE.

>>47690415
We honestly don't know.

It has nothing to with probability. If it can be rolled for infinity, it will roll a 1. When talking about infinity, anything that CAN happen, WILL happen. It will also land on it's edge eventually.

Since our atoms cannot be destroyed (if I remember it right), the earth will eventually be destroyed, and it will eventually be put together again, exactly the way it was. It will also be recreated with slight differences, for example, with dragons instead of people. But that's a big if. If time is infinite, if matter cannot be destroyed, everything that can happen, will happen. I will have sex with each and everyone of you. Probably not you in your current life, but the recreated version of you, with the same memories, same family and same atoms that make up your body right now. I'll even fuck your mom.

>>47690424
Atoms can be transformed, hence e=mc^2. Energy in the universe is constant though

>>47690424
>Since our atoms cannot be destroyed (if I remember it right),
Energy can't be destroyed or created (unless zero-point energy actually pans out to be real shit); atoms can be reduced to their constituent fundamental particles and annihilated via matter-antimatter collision.

>>47690424
>When talking about infinity, anything that CAN happen, WILL happen.
... Oh yeah? Does that include for every single of the infinity d20 rolls to come up 20? Will that inevitably happen?

>>47690424
>When talking about infinity, anything that CAN happen, WILL happen.

[citation needed]

this is some deepak chopra style bullshit

>>47690447
>annihilated via matter-antimatter collision
"Annihilated" in this case means being converted to energy, right?

>>47690485
Yes; in fact, this happens all the time on the quantum scale; matter-antimatter pairs of elementary particles spontaneously come into existence, only to immediately annihilate each other moments later.

>>47690485
yes duh

Where do you think the energy from antimatter explosions come from?

All depend of how infinite its your infinite

File: 1463233358006.jpg (60KB, 800x638px) Image search: [Google]

60KB, 800x638px

you guys are all fuckin' nerds

>>47690483
x^y=0 when y approaches infinity for any 0<x<1

>>47690559
Where do you think you are, /fit/?

>>47690493
Isnt that a bit like hawking radiation, which isnt well proven?

>>47690559
"Nerds" would imply that almost half of us know what we're talking about. The term I would use is "dweebs."

>>47690635
In general terms, Hawking radiation is what happens when a matter-antimatter pair is spontaneously created, but one particle is sucked into a black hole and the other is just far enough away that it heads off somewhere else. As far as I'm aware it's too small of an effect to actually be measured.

>>47690690
I heard there was some critisism of the hawking radiation theory, but im no physicist

>>47689857
Well, yeah the chance on any individual roll is 5%, but if you roll 2 d20 you have 20^2 possible reults and only one of them is 2 times the 1. So your chance of getting 1 1 when rolling two dice (or one dice twice) is 1/(20^2) or you can multiply the chances 0.05 * 0.05. The chances of each dice throw are equal, but getting always the same number is getting more and more unlikely to the point it is basically 0.

That guy >>47683780 did the math right as far as I know

>>47684333
I thought the idea of shrödingers cat is not to view the cat as an microscopic entity, but binding it to one. Basically making the state of the cat dependant on the decay of radio active matter.

>>47690483
Just take a look at the hyperwebster
https://youtu.be/s86-Z-CbaHA?t=9m32s
It's about an infinite dictionary. And the result is: Everything that has, can and will be written is in there (Well everything using our alphabet).

holy fuck this is ridiculous

if you role a theoretical dice an infinite number of times you will get a result of 1 an infinite number of times

welcome to infinity

>>47690534
>All depend of how infinite its your infinite
>>47690424
>If time is infinite, if matter cannot be destroyed, everything that can happen, will happen. I will have sex
Not THAT infinite.

>>47690424
>It has nothing to with probability. If it can be rolled for infinity, it will roll a 1. When talking about infinity, anything that CAN happen, WILL happen. It will also land on it's edge eventually.
There is also infinite amount of dice being rolled infinite amount of times and thus there will be one that never rolls a 1 by this very logic.

>>47691559
see
>>47691559

>>47691559
That's the one where the one didn't get print on correctly senpai.

Seriously, if you want to know if it's possible:
>Take a dice
>Throw it until you get an 1
>realise that somewhere in the infinite sequence of rolls the exact sequence you just rolled can be found

>>47691574
Nice recursion.

>>47691581
Nope.
If ANYTHING can happen, then a no-ones can also happen.

>>47691559

you cant apply the word 'never' to infinity because infinity is by definition never ending

Oye
>>47691574
See also
>>47683939

>>47691599
>Nice recursion.
Heh

>>47691600
And in the infinite dice there will be a die that will just keep rolling anything except 1s. Forever.

For any die that has a sequence of rolls that aren't ones that end with a one, there is also another die with the same sequence but that doesn't roll a 1.
Because infinity, mothefucker.

>>47684162
>Roll a D20 an infinite number of times

did you even read what op said?

>>47683615
No, that would contradict the Law of Large Numbers
>>47683740
You wiill NEVER roll a 21 on a d20 after an INFINITE number of rolls.

The die has no memory, so there's nothing forcing it to roll 1 at any point. However probability of such a sequence is (0.95)^infinity which is infinitely close to zero.

But after each time you rolled not 1, your probability to continue the streak does not actually decrease.

>Is it possible to never roll 1 with an infinite number of rolls ?
No
>Is it possible to never roll 1 with a very large number of rolls? (example : 99999999999999999999999999999999999999999999999999999999999999999999999999 rolls)
Yes.

>>47691647
THEORETICALLY THE DAMAGE ON THE DIE FROM ENDLESS ROLLING MAY CREATE CRACKS ON THE SURFACE THAT TURN ONE OF THE OTHER NUMBERS INTO 21 AND THEN BE ROLLED

>>47691628

no you cant apply time-scales to infinity 'forever' doesnt exist as a concept within infinity

infinity will exhaust all possible outcomes an infinite number of times, that is infinity, you're trying to draw an arbitrary line and saying that THIS specific dice hasn't rolled anything but a 1 an 'infinite' number of times, but while you're saying that the dice is still rolling and will always roll

infinite dice will roll a consecutive number of 1s proportionate to any number that can be fit within the universe

however, an infinite number of dice cannot roll 1s infinitely because the very idea of rolling the same number infinitely is absurd

>>47683780
this is the correct maths

>>47691694
Or just the good old "it splits down the middle and the two top sides add up to 21"

>>47691697
Your logic a shit. You declare "ANYTHING can happen because infinity" but then say that a thing can't happen because infinity.

Check yer m8.

>>47691683
This. In infinite rolls 1s will always be 1/20th of the rolls. But finite sequences will have all sorts of deviations.

t. Someone who heard about probability theory once in 8th grade

>>47691722

its not, you're just married to your incorrect idea because you dont want to be wrong on the internet

i never said "anything can happen" i said "all possible outcomes will be exhausted" those are two completely different statements

now a dice has 20 posible outcomes, roll it an infinite number of times and all of these outcomes will occur an infinite number of times

therefore the idea of a dice rolling 1 'infinitely' does not work, no matter the scale upon which you roll dice

>>47683615
Yes it is possible, with a chance of 0 of it happening. (ain't infinities fun)

>>47691675
Again, it has been said at least twice in the thread.
The probability for any single roll to get a specific side on a d20 is 0.05 or 5%
The set of results on one throw of an d20 is 20, and one of those is 1, hence we have on a single d20 a chance of 5%
The set of results on two throws of an d20 is 20*20, and only one is 1 1, hence we have on two rolls a chance of 0.25% (1/(20^2))

The probability of a single roll stays the same, but while the set of results grows with every roll we always only have one favourable outcome, hence the overall probability sinks.

But the actual way to solve that would be the lim of the throws, which is 0, which has also been said a few times here.

>>47683932
This guy has it right, but all of these other posters are too hung up over the difference between a chance of zero, and an impossibility. (which a chance of zero isn't)

Take a dartboard for example, the chance for a dart to hit any place on it is proportional to its area yes? points do not have area, so the chance for a dart to hit any specific point on the dartboard is zero, yet clearly any of those points are still valid places for the dart to hit.

>>47683997
Which is the same number but represented differently. (also 0 repeating but a 1 behind is stupidly poorly defined)

>>47683615
The answer is yes and no.
Both are theoretically possible, infinity is a weird 'value' in that way.
1+Infinity = Infinity
Infinity - Infinity =/= 0,1

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Are people serious.

You roll a dice infinite amount of times, thus you get an infinite amount of numbers that may happen. Thus, because you keep rolling infinitely, you will get a 1 eventually at some point along the line.

For fucks sake this is simple, don't make it deeper than it has to be.

>>47691943
this, really.

>>47685199
>This is opposed to uncountable infinities in which it is impossible to put that infinity, or any subset or interval of it, into one to one correspondence with the set of natural numbers.

This is blatantly false, the natural numbers are a subset of the real numbers, and that subset is obviously in a one to one correspondence with itself. (This obviously isn't true for arbitrary subsets of the real numbers tho)

>>47690341
Except we are already talking about infinities, and representing our chosen number was never a necessary part of this. (we have infinite ways to represent any number anyways, so its moot to begin with too)

>>47691525
The schrödinger cat experiment is merely a thought experiment to showcase the weirdness that lies in quantum mechanics. It has no relevance to physical experiments.

>>47692141
Well, yes of course. If that was his point I guess I have missed it

>>47691943
There's an infinite number of infinite sequence of values between 1 and 20 that do not contain a 1.
There's infinitely more sequences DO contain a 1.

Ergo, it is possible for a die to infinitely not roll a 1, but the chance is 0 (because the proportion of sets carrying that property is 0)

In a similar way, 100% of all numbers contains a 3. I can show an infinite number of counterexamples, but for any number the chance of not containing a 3 is 0. Yet numbers such as 2, 5, 667986876 etc. do exist.

>Roll a d∞.
What number do you roll?

>>47692253
6

>it's this "freshman discovers math" thread again
STOP
FUCKING STOP

>>47692253
Aleph-0 or Aleph-1, obviously.

>>47692253
A dang, I rolled Abs[∞ - ∞], now how do I figure out my stats?

Rolled 11, 12, 14, 16, 1, 19, 2, 8, 2, 1, 17, 13, 4, 20, 19, 16, 15, 16, 3, 19, 9, 18, 4, 2, 15 = 276 (25d20)

>>47683615
Let's see...

>>47691826
That's not the probability of rolling at least a single 1 in X rolls, it's the probability of only rolling 1 in X rolls.

>>47690341
>you cannot randomly select a real number, as it is impossible to describe one

Bullshit. I just write "pi". Or "5", which of course perfectly describes 5.0, 5.00, and so on, all of which are the same number, not different ones. Or I write "2^(1/2)". There are still an uncountably infinite number of real numbers with exact representations, even if you're still missing the uncountably infinite set of numbers we haven't bothered to come up with exact representations for.

Your problem is thinking you have to put a number in un-rounded, decimal form, to infinite precision, in order to represent it. That's just not so.

My point is that proving that OP describes a zero probability event doesn't actually answer the question.

>>47692218
There's only one infinity here. No TWO infinities, or THREE. There's ONE infinity that's INFINITE, thus you will get 1 INFINITE amount of times.

This isn't about philosophy, you roll ONE DICE INFINITELY. The sequence or anything else doesn't MATTER because you DON'T STOP ROLLING THE DICE.

IT IS NOT POSSIBLE TO NOT! ROLL A 1 ON AN INFINITELY ROLLING STREAK.

>>47692333
Oh right. Guess I should pay more attention sometimes. Sorry.
But still the chances of the streak continuing is always decreasing, and the limit of it is 0. Its just decreasing way slower, since the probability of not rolling a one is 0.95.
lim n->inf (0.95^n) = 0

>>47691559
>anything that CAN happen, WILL happen
This includes the never ever rolling a 1 or even only rolling a 1

>>47692435
The things that CAN happen on a d20 are:
>Rolling a 1
>Rolling a 2
>Rolling a 3
>Rolling a 4
>Rolling a 5
>Rolling a 6
>Rolling a 7
>Rolling a 8
>Rolling a 9
>Rolling a 10
>Rolling a 11
>Rolling a 12
>Rolling a 13
>Rolling a 14
>Rolling a 15
>Rolling a 16
>Rolling a 17
>Rolling a 18
>Rolling a 19
>Rolling a 20
And of these, all WILL happen an infinite amount of times.

>>47692415
Pssh, pleb doesn't realise there's Infinite kinds of infinities.

>>47683615
No, because probability of rolling 1 is converging to 1 as number of rolls goes to infinity, and when you are making passage to the limit, probability of rolling 1 goes to 1.

>>47685887
Anon, pimping ain't easy. Most of 'em fleece me every night, in fact.

>>47692253
Which infinity? As >>47692298 mentioned, there is an infinite number of infinites, one is larger than other.

>>47686519
Trees, anon.

>>47683685
So is doing anything an infinite number of times.

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>>47683755
>>47683745
>>47683737
>>47683691
>>47683676
>>47683659
>>47683626

Is this trolling or have I been drastically overestimating the intelligence of elegan/tg/entlemen?

Assuming that the die and the roll are fair and that the die and rolling apparatus are made of some hypothetical material that can withstand an infinite number of rolls without deforming or wearing away then all non-zero outcomes will occur and infinite number of times.

Infinity divided by any real number is infinity. Technically you will roll the 20-2 edge an infinite number of times, you will roll the 2-18-4-14-20 vertex an infinite number of times.

Having a random outcome select unfairly is only possible for finite numbers of rolls.

>>47692475
With a chance of 1, or almost always.

Please do distinguish between events with chances of 1 or 0, and events that can't happen or will always happen. Since they are absolutely not the same.

The chance that a number amongst the countably infinite natural numbers contains a 1 (or any other digit) is 1, and corollarily the chance of not containing a 1 is 0 , however clearly numbers that do not contain a 1 exist. (there are even countably infinite amounts of them in fact)

There's a reason that the term "almost always" exists in mathematics. And in this case, almost always does an infinite sequence of rolls on a d20 contain at least one 1. But an infinite sequence without a one is still possible. (with chance 0, or almost never)

>>47686179
> mathematicians were originally pretty suspicious of limits at first because this seemed like a weird, half-assed way to go about things
I remember the other story - they were suspicious about using infinitesimal and infinite numbers, and using limits was hailed as the only true way until 1950s or so, when non-standard analysis came back into style.

>>47683615

Yes. All it requires is for you to be infinitely unlucky.

>>47683615
ITT: people think infinity is a big number.

>>47692564
>with chance 0, or almost never
Chance 0 is never. This sequence converges to zero as number of rolls goes to infinity.

>>47683615
I believe the answer is no.

If you roll something an infinite number of times, probabilities stop being guidelines and start smoothing out the distributions of results.

Now, should you have said "some profusely large number", then theoretically it's possible, but "infinite" is where things get tricky.

>>47683783
If reality is an expression of true randomness then an infinite reality would contain an infinite number of every potentiality. Which means that it is very likely that the universe is either not truly random, as root 2 or pi or natural log are not random but infinite, or the universe is not infinite or both.

>>47683932
If you use standard analysis. In non-standard one it is possible to have an infinitely small non-zero probability... but then you are taking standard part of it and have zero again.

>>47683615
No. You roll the dice an infinite number of times and it will land on 1 an infinite number of times.

It will also land on one of the points and fucking stand there an infinite number of times.

>>47688637
Then the answer isn't 'yes you can' it's 'the situation is impossible'. I have no idea how you word it in statistician speak, but the intent of anon is obvious. It's not the physical act of rolling a d20 infinite times, its 'can an event with a 1/20 chance of occurring never happen if there are infinite chances of the event occurring?' or again, however the fuck you say it.

The answer is no. The limit of 0.95^n approaches 0 as n tends to infinity, so if you say n=infinity, the probability is 0.
>>47688747
There's no such thing as an infinite amount of zeroes with a 1 on the end anon, since that implies there is an end, which completely ignores the concept of infinity (endless).

>>47690268
Not that anon but you're dead wrong. Infinity is not a counting number. One divided by infinity isn't "close to zero" it IS zero. Ghram's number divided by infinity is zero. Any arbitrarily large number divided by infinity is zero.

>>47688825
Yes, but physics deals with real numbers. In maths (which is what we're dealing with) the chance is zero, because you're dealing with a true infinity, not just 'a very big number'.

>>47683900
That's true for any countable number of steps. And infinite number of steps is not a countable number of steps.

>>47692713
>And infinite number of steps is not a countable number of steps.
It may be. Natural numbers are countably infinite set.

>>47690477
Not every single roll no, since that's impossible as said above. But there will be an infinite number of 20s, and every other number from 1-20 for that matter.
>>47691559
Except that's impossible, as said above. It's everything that can happen, not just everything.

>>47684187
I think he was trying to be poetic.
Also I have no idea what infinity divided by infinity would do.

>>47692564
>With a chance of 1, or almost always.
Chance of 1 is always anon, not almost always.

>>47684142
>It's waiting for us at the end of infinity.
Infinity, by definition, doesn't have an end.

Likewise, if it has an end, it isn't infinity.

ITT: people don't understand that 0.(9) = 1.

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>>47685887
>The better question is, as X approaches infinity, does pimping become easier?
Hell yeah.

>>47692533
>Anon, pimping ain't easy.
Citing precedent to the contrary
>>47683951

>>47684403
>This is not always right either.
It's not always right, no, but it's right noticeably more often than it's wrong.

>>47692848
See
>>47692797
>I think he was trying to be poetic.
And also
>>47689180

>>47686594
>What if I wanted a goat, fag?
Then after you win the money, spend some of it and buy a goat.

Like, goats aren't expensive, just go to a farm.

>>47689296
>But there is still a difference between "three thirds" and "0.999...".
>Just not an effective one.
There is zero difference between three thirds and 0.999... . They are the same number.

>>47692821
You are wrong
Here's why:
https://en.wikipedia.org/wiki/Almost_always

The chance of rolling a 1 is 5% or 1-(chance of not rolling a 1).

.05x.05x.05.... is not the chance of rolling at least a single 1 in infinite rolls, the proper equation would be 1-(.95^infinity). .95^infinity has a limit of zero, so 1-0, thus an infinite number of dice rolls had a 100% chance of at least one of those rolls being 1

>>47692996
>>47689608
Switching doors doesn't change the probability that you first picked the winning door.
The probability that the first door you picked was right is less than the probability that the only other door remaining after all the others were randomly eliminated.
Unless you have the right door all the time, in which case it doesn't matter how many other doors were eliminated.
In the end, the final choice is between two doors and it's 50-50.

>>47693215
important bit there:
>In probability experiments on a finite sample space there is no difference between almost surely and surely, but the distinction becomes important when the sample space is an infinite set (because an infinite set can have non-empty subsets of probability zero)

>>47693140
>There is zero difference between three thirds and 0.999... . They are the same number
Only if you believe "1" stretches to Infinity.
Slicing the number one into thirds creates three numbers that stretch into Infinity. Only by undoing that process can you restore the number one to its whole self and not .999...

>>47693279
You simply can't see the difference between a number and its representation. 0.9999... at infinitum and 1 are just two representations of the same number.

>>47692797
> infinity divided by infinity
it's not defined

>>47693379
So you *do* believe that 1 stretches on into Infinity.
That's okay. I'm not here to question people's beliefs.
I'm just here to point out the truth.

>>47693443
>So you *do* believe that 1 stretches on into Infinity.
If it does (by one way of writing it) what's the issue with that?

>>47693463
>If it does (by one way of writing it)
(Speaking of the difference between a number stretching to infinity and its representation stretching to Infinity)

>what's the issue with that?
No real issue. It's just that if 1 does not stretch to Infinity that is a pretty big difference between it and 0.999...

>>47693443
The proper term is 'irrational'. You can have finite, well-defined numbers be irrational.

>>47689608
Each door would have an equal chance IF there was a 1/3 chance of monty picking the car, but he will always open a goat door. He knows what is behind the doors.

If we expand the problem to 10000 doors and you have to pick which one has the prize you start and pick with a one in 10000 chance of being correct. Then a man who knows whats behind all the doors opens up all but one other than the one you picked. He knows where the prize is and makes sure not to reveal it. So which of the two remaining doors has better odds of containing the prize?

>>47693524
1 = 1.0 = 1.00 = 1.000 = 1.0000 = 1.00000 = 1.0000000000000000000000000...
=0.9999999999999999999999999....

>>47693524
>It's just that if 1 does not stretch to Infinity that is a pretty big difference between it and 0.999...
Nope, no difference. You can write it as a recurring decimal, or you can write it as just 1, but either way is a valid representation of the same number. 3*(1/3) is both 0.999... (since it's 3*0.333...) and 1 (since 3*(1/3)=3/3, and any number over itself is 1).

So your choices are either to argue 3*(1/3) equals two different numbers at the same time, argue that my maths is wrong, or concede that 0.999...=1. Your choice.

>>47693559
>You can have finite, well-defined numbers be irrational
People can be irrational too.
Do you believe that 1 is irrational?
Do you believe that 0.999... is?

>>47693617
Yeah, this is the practical truth.
That's why I've been imagining Deal or No Deal with the briefcases and Howie Mandel
But Monty Hall is more tg

>>47693668
So you believe all numbers, not just their representations, are infinite then?

>>47693669
>3*(1/3) is both 0.999... (since it's 3*0.333...)
I am disagreeing that 0.333... is equal to 1/3.
One forms a rational number when multiplied by 3, the other does not.

>>47693886
But remember, I said earlier that they are *effectively* equal.

>>47693785
I mean it's the monte hall problem. If the host has a chance of accidentally revealing the prize then yes, you don't need to switch and all odds are equal. I just find that making the scenario more dramatic draws into relief what the host's knowledge adds to your decision making.

>>47693886
Then what is 1/3 expressed as a decimal?

>>47694181
>Then what is 1/3 expressed as a decimal?
Answer: Inaccurate

>>47694125
True.
It's an excellent example of the folly of focusing so hard on probabilities, that you lose sight of the reality of the question.

>>47694321
Assuming you're saying 1/3 can't be expressed as a decimal, or that .3 recurring is different to 1/3, nonsense. 1/3 is .3 recurring in the same way 1/2 is 0.5, or 1/10 is 0.1, or 1/7 is 0.142857 recurring. They're different ways of expressing the same number. You can do the maths yourself if you want, try long dividing 3 into 1.

>>47683615

no, if you are rolling an infinite number of times the dice will land on every number an infinite number of times. You're even bound to get a few 21's

>>47684162

infinity is exactly impossible, that's the whole point. Over the course of rolling a d20 an infinite number of times, you not only roll every number possible, but every number that is impossible too. This is because you are multiplying every single possibility, no matter how small, by certainty.

it's possible that a series of unfortunate events will cause the dice to break the speed of sound and pierce the skull of John Oliver, so multiply that tiny, almost insignificant chance by absolute certainty and it isn't just possible, it's inevitable.

>>47694542
>Over the course of rolling a d20 an infinite number of times, you not only roll every number possible, but every number that is impossible too.
Something impossible won't happen no matter how many times you roll. Given it's able to resist the stress of being rolled infinite times, it's not changed by being rolled, so you can't even pull the 'oh but it might crack and turn the 20 on it into 21' card.