If I keep throwing a dice with infinite number of sides, each

>>8541661
[math]\mathbb{N},\, \mathbb{Z} [/math] or [math]\mathbb{R}[/math] numbers?

>>8541953
The first 2 options are the same you brainlet N is in bijection to Z and Q

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>near-infinite

>>8541959
Something like infinity minus 5 probably.

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>>8541661
Idk... the probability of getting any specific number approaches zero.

>>8541997
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%).

>>8542020
But an infinity-sided die (just realized my pic was actually related) would give each number an infinitely small chance of occurring.

>>8542028
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.

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>>8541955
>N is in bijection to Z and Q

>THEREFORE THEY'RE ALL THE SAME LOL

This is why nobody takes mathematicians seriously.

>>8542045
Good thing countably-infinite-sided dice don't exist.

Use sequence limite to calculate it. (I am curious, I will try)

>>8542062
everything exists in math once it is defined you gay brainlet

>>8542078
Define "a dice with infinite number of sides."

>>8542083
That argument can be used on anything.

Define 'monkey'.

>>8541661
I think theres a higher chance of it repeating the same number forever

>>8542083
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

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>>8542087
>Good thing countably-infinite-sided dice don't exist.

>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

>>8542087
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.

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.

>>8542135
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 ?

>>8542062
isn't a ball an infinite-sided ""dice"" ?

>>8542140
> 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

>>8542145
A ball is made out of a discrete number of subatomic particles. So, no.

Well, suppose your probability would be 1/infinity so 0%

Haha gottem l o l. I'm so smart

>>8541661
>a dice

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>>8541975
>infinity minus 5

Are you fucking retarded! Holy Kek, my sides

>>8541661
If thrown infinity amount of times there will inevitably be a combination of two identical rolls

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

>>8542408
Tl:dr rolling a one sided sphere with every number to infinity written on its surface

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.

>>8542140
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

>>8541661
A dice with infinite sides has an infinitely low chance of landing any particular number so you can never roll anything

>>8543972
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

>>8543835
I think you're onto something but the equation keeps getting longer the higher n is

>>8544027
>>8543835
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%

>>8541661
My mind says yes, but my gut feel says no.

>>8542408
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

>>8544162
The probability of it landing on the same number is 1 every time