This scenario seems to indicate a problem with the concept of an infinite-sided die, possibly even suggesting that such a die cannot exist. — keystone
"Infinite" is not a number as an amount of sides but is that which cannot be gotten to since it never completes, but to play along, the die is ever becoming more of a higher and higher resolution smoother sphere. — PoeticUniverse
There would be no way to read the numbers because any of them could appear to be unlimited and by the physical limitations of the universe would therefore be impossible. — Nils Loc
Is this truly a paradox? If not, why not? [...] This scenario seems to indicate a problem with the concept of an infinite-sided die, possibly even suggesting that such a die cannot exist. What are your thoughts? — keystone
only a finite number of outcomes were lower, yet an infinite number were higher, making the serpent's probability of beating him exactly 100%. — keystone
Just as a polygon with infinite sides of equal length would be empirically indiscernible form a perfect circle—this irrespective of how close one observes it, say with a quantum microscope—so too would a die with infinite sides of equal length be empirically indiscernible from a perfect sphere, even when analyzed with a quantum microscope. — javra
The limitation of possible representation is still an issue here; there must be a finite maximum magnitude for the game. Infinity cannot be a stipulation. — Nils Loc
You could fix the problem with doing away the limit of natural numbers and including the negative integers to infinity. — Nils Loc
Maybe it's undefined for the natural numbers also. — Nils Loc
All that's left is a little divine magic to ensure it rolls fairly, and extraordinary vision for the players to discern the minuscule markings on those higher rolls. — keystone
It probably doesn't make sense to roll an infinite sided dice in the first place — flannel jesus
In that case, I’ll let this thread be. But I confess, to me, this conflux of mathematical thought with “magic” and “extraordinary vision” not bound by empirical sight so far equates to the question of: What defined result obtains when one divides three and a quarter invisible unicorns by zero? Just saying. — javra
If you believe that infinite sets cannot exist, then I am preaching to the choir. — keystone
I guess you mean this post. This doesn't seem like a paradox to me. Where do you think the paradox is? — flannel jesus
Just to be clear: when it comes to the realm of pure mathematical thought, I can see it both ways and so remain on the fence; but when it comes to empirical reality as in the form of a die, a member of the just stated choir I am. — javra
Do you believe that the set of all natural numbers exists? Is it reasonable to stipulate its existence? If infinite sets can exist in some realm, why can infinite dice not exist in God's realm? — keystone
Infinity is an unreasonable stipulation and whether or not numbers "exist" is not all that relevant to me. The natural numbers definitely have a limit of physical representation and there'd be an infinite amount of numbers beyond that limit. — Nils Loc
[...] it could just as easily have been described purely as a mathematical problem within the realm of abstract mathematical thought. Indeed, when you questioned the feasibility of constructing such a die, it seemed you were addressing the narrative element of the paradox, leaving the core mathematical issue untouched. — keystone
One can simplicity the very same issue by addressing the purely mathematical concept of a perfect circle and its nonexistence in empirical reality. — javra
The real question isn't whether quantum mechanics is fictional (an idea that seems absurd), but rather if quantum mechanics employs the infinite-rooted objects themselves or merely the finite descriptions of — keystone
My own slant is that in physical reality there can be no absolutely integral physical being as is symbolized by the number one/1 when the issue is addressed more objectively — javra
As regards infinities, if you happen to not be familiar with them, you may get a kick out of surreal numbers. — javra
Well your mistake is assuming it drops to 0%. If the die is split the way you said, it absolutely does NOT drop to 0% unless he rolled a 1. — flannel jesus
You could only make a good argument that it drops to 0% if every number on the die had an equal probability - but the die you laid out does not have that feature. — flannel jesus
Doesn't the effectiveness of classical computers contradict your perspective? — keystone
The probability of Adam winning is exactly 0%. — keystone
When I mentioned that the dice with infinite sides are fair, I was specifically referring to each side having an equal chance of being rolled. After all, God is fair. :P — keystone
Then why did you point me to your post where 1 takes up half the space on the die — flannel jesus
Is this truly a paradox? If not, why not? — keystone
With trepidation, Adam opened his eyes to see a googolplex dots on his die. It dawned on him then: with his roll being finite, only a finite number of outcomes were lower, yet an infinite number were higher, making the serpent's probability of beating him exactly 100%. — keystone
Now, putting trivial matters aside, do you understand that Adam's probability of winning becomes exactly 0% once he sees his roll? If you disagree, what do you calculate his probability to be? — keystone
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