If I keep throwing a dice with infinite number of sides, each side representing a unique number, is it possible to get same numbers if I just keep throwing for a very long time?
What's the logic on this. Like, the problem is easy if there is near-infinite amount of sides, right? Then you eventually start to get same sides.
Ian Anderson
[math]\mathbb{N},\, \mathbb{Z} [/math] or [math]\mathbb{R}[/math] numbers?
Ayden Wright
The first 2 options are the same you brainlet N is in bijection to Z and Q
Mason Howard
>near-infinite
Justin Smith
Something like infinity minus 5 probably.
Austin Price
Idk... the probability of getting any specific number approaches zero.
Noah Howard
Yeah but then again, if it is truly random dice, every side has equal chance of happening right? Regardless of what has been thrown before.
So let's say I throw the dice and get number 6. Surely the chance to get number 6 cannot be exactly 0%, because then every side would have 0% chance to occur. So it should be higher than zero, even though very very small.
Every time I throw the dice it gets more likely that I get same number because the pool of same number grows (with each having probability higher than exactly 0%).
Samuel Perez
But an infinity-sided die (just realized my pic was actually related) would give each number an infinitely small chance of occurring.
Christian Butler
That's true. But that's pretty strange. I wouldn't be able to throw the dice, or if I threw it, it would land on no side.
Logan Reed
>N is in bijection to Z and Q
>THEREFORE THEY'RE ALL THE SAME LOL
This is why nobody takes mathematicians seriously.
Levi Kelly
Good thing countably-infinite-sided dice don't exist.
Jordan Flores
Use sequence limite to calculate it. (I am curious, I will try)
Camden Hill
everything exists in math once it is defined you gay brainlet
Jackson Murphy
Define "a dice with infinite number of sides."
Evan Ortiz
That argument can be used on anything.
Define 'monkey'.
Luis Parker
I think theres a higher chance of it repeating the same number forever
Evan Peterson
s is the number of face of the dice.
A dice with infinite number of sides is equal to \lim\limits_{\substack{s \rightarrow \infty }} dice
>everything exists in math once it is defined you gay brainlet
>Define "a dice with infinite number of sides."
>lol nah bruh, that's a fallacious argument
Michael White
Of course you could use the concept of monkey in math. If it is defined properly. Monkey is just a word, and it is arbitrary to use a word and not another. Therefore it does not matter in math.
Evan Stewart
Infinity isn't really a number, it's more like a hypothetical value. My own take on this phenomena is that when a finite value is compared to an infinite one they behave in a similar manner as 0 does to a finite value. So while it isn't necessarily impossible for the die to land on the same side twice it's infinitely improbable, so it's impossible in a practical sense.
Daniel Garcia
That reasoning is correct with a finite amount of attempts.
The real question is : what happens when you throw your dice an infinite number of times. Wich inifinity beats the other ?
Grayson Scott
isn't a ball an infinite-sided ""dice"" ?
Blake Bennett
> Wich inifinity beats the other ? you have to count past-infinity, you could try to build a biyective function to see which one is bigger
Luke Jones
A ball is made out of a discrete number of subatomic particles. So, no.
Liam Morris
Well, suppose your probability would be 1/infinity so 0%
Haha gottem l o l. I'm so smart
Cameron Butler
>a dice
Logan Lewis
>infinity minus 5
Are you fucking retarded! Holy Kek, my sides
Aiden Cooper
If thrown infinity amount of times there will inevitably be a combination of two identical rolls
Ryan Thomas
It would never land on a side, another way of representing this is if you look at the energy required to tip a six sided die over to the next value, then a 8 sided die, then a 12 sided die, then a 20 sided, the energy decreases as the face diameter decreases in relation to the centre of mass, as the number of faces increases to infinity the amount of energy required to turn the die to the next number decreases to zero, resulting in one energy state encapsulating all the numbers, on every die roll all the numbers come up at once, you have 100% chance of rolling the same number every time
Brayden Myers
Tl:dr rolling a one sided sphere with every number to infinity written on its surface
Jeremiah Martin
I have found.
If you define n to be the number of trial you have and s to be the number of sides of your dice, then the chance to land a preedermined choosed number is equal to 1 - ( 1 - ( 1 / s ) ) ^ n )
Now, it depends on how s and n will be infinite. If the goes infinite exactly at the same speed (s=n), the probality is 1- 1/e = 0.63, but it kinda of means nothing.
Benjamin Anderson
I actually used to think about this a lot regarding the multiverse theory, how people say "every possible universe exists in the multiverse, thus my waifu is real somewhere". If some kind of higher dimension or entity continued creating new universes infinitely with the starting conditions altered slightly from the last, would that really mean that every situation is bound to happen eventually?
so I started thinking about what the probability of randomly drawing a specific value in a pool of N values given N trials would be. I can't remember my equation, but N=2 is 2+1 / 4 = 3/4 N=3 is 9+3+1 / 27 = 13/27 N=4 is 256+16+4+1 / 1024 = 277 sorry I'm a noob, haven't done stats yet
Parker Gutierrez
A dice with infinite sides has an infinitely low chance of landing any particular number so you can never roll anything
Blake Ward
wait hold up my equation here is wrong, I was doing 1/n + 1/n^2 + 1/n^3 ... n times but actually the equation is should be 1/n + (n-1/n)/n + (n-1(n-1/n)/n)/n ... n times
I think you're onto something but the equation keeps getting longer the higher n is
Aiden Baker
wait nvm you were right I ended up with summation of (n-1/n)^x)/n for x=0 to n-1 which is pretty much the same thing as your equation so yeah it looks like as n approaches infinity the probability of drawing n in n possibilities with n trials decreases toward 63%
Jacob Roberts
My mind says yes, but my gut feel says no.
Hunter Perez
I've answered it perfectly here, a die with intimate sides would behave as a sphere and would not ever roll on a particular side, the thermodynamic energy required in a system to not have enough energy to topple to the next face would be infinitely small,
it would behave as a one sided sphere with every number from one to infinity written on its surface
Jordan Phillips
The probability of it landing on the same number is 1 every time