Infinity

#11

Ok maybe i'm just stupid, but that sounds completely wrong to me. If you rolled the dice an infinite amount of times, you would most certainly roll an infinite amount of all 6s (and every other combination), the math you are applying to it has no real bearing here. This is much more of a philosophical question than it is a mathematical question. At some point you are making infinity have some finite bounds, which means you arent talking about infinity, you are talking about a very large amount of repetitions APPROACHING infinity. But if it was possible to extrapolate the set of rolls to actual infinity every possible roll would exist (along with ever possible FINITE series of rolls that never come up all 6s), if you were to apply any finite value I would agree, but as long as the amount rolls is infinite, than the amount of 60s rolled is as well. If you were to say within infinite rolls is there the possibility of (insert any finite number here) rolls without all 6s happening, I would agree that that possibility would also exist within the series. BUT, there is no way you could roll the dice an infinite amount of times without every possible outcome presenting itself an infinite amount of times.

#12

QUOTEthere is no way you could roll the dice an infinite amount of times without every possible outcome presenting itself an infinite amount of times.

you need to read about the differences between infinity and the cardinality of infinite sets.

1. "impossible" is a word that NEVER applies with regard to INFINITY, as a mathematically philosophical construct. Probablity is a value, and even if it is valued at 0, it still does not indicate "impossible."

You are talking about a infinite set of occurances of an array of 50 values (10-60) which we will call x that has a cardinality of at least 300(∞).

Thus, you are not talking about an infinite number of rolls, but an uncounted and unending series of rolls which represent all of the possible results evenly in a perpetually equal and exponential series. mathematically, this would be:

x = 300(50*∞)

or 50x = 6(1*∞)

that is to say 6/(50/x) = ∞

Having an infinite set is different than having an infinite count of a finite array of 50 results (10-60). Your infinite set has a cardinality of 50. by the statistics involved in Uspensky's work on dice rolls and frequency of result, a result of 60 (the terminal high value) of the array is not nearly as common as many other values. And there is nothing that says EVERY RESULT IN YOUR ARRAY MUST OCCUR. nothing at all.

#13

Ok can we just drop the math? I mean it really has no meaning. You cant say that "36/(50/x) = ∞ " thats just not even close to true(unless x=∞). If you were to roll dice an infinite amount of times every possible outcome would express itself an infinite amount of times, that being said, logically you cant have the dice come up infinitely all 6s, and yet within the same set never have 6s at all. You have to side of the inevitability of it coming up all sixes. But this in and of itself may be a restiction of infinity. It seems to me you are using rules you have been taught somewhere that really dont apply to the matter at hand. I dont care what the current understanding of mathematics is, i'm talking about the philosophical infinity, not the one that has "cardinality". By establishing any sort of cardinality, you are giving a direction to something that is omnipresent.

#14

But how can probability not be implied, even in an infinite set, if it is possible you could roll the dice an infinite amount of times and never get a 60..? That's what I think he's trying to say, more or less...

If you roll the dice an infinite amount of times, you are not guaranteed to even get a 60...So, that said, how can you get any specific amount, when that amount is not 100% certain to be achieved..? Without probabability (the math) you have to provide logic that says more than the assumption of rolling a 60...You could very well roll the dice an infinite amount of times, and not come up with several variables...As he said, there's nothing that says every result in the array must occur...

#15

whelll then,.. if we are going to drop the mathematics, and forget about the 50 possible results of a roll of 10 six sided dice,.. you have an infinite number of 10 dice rolls resulting in banana and green and as well as your infinite result of 60.

there is nothing NOTHING AT ALL THAT SAYS AN INFINITE REPETITION OF A SINGLE ACTION (such as a roll of ten dice) MUST RESULT IN ALL POSSIBLE OUTCOMES. Plainly put, the number of repetitions does not influence the likely hood of a particular outcome unless you have other varying factors that change. The ABSOLUTELY EXACT conditions will OCCUR IN THE SAME OUTCOME. You can not even begin to presume you will see a sixty if you have no means of increasing the probability of the result of 60. with varying factors, you will lose the consistency of any given result, and thus - look at the

you have given sample values, for your ten dice: each has its limits of 6 values.. this results in 50 possible outcomes,.. an array of the real whole numbers 10 through 50.

When you have defined ∞ as the value of the number of repetitions,.. and you further establish that (in your assumption) all of your FIFTY OUTCOMES are EQUALLY REPRESENTED...

as you said:

QUOTEIf you were to roll dice an infinite amount of times every possible outcome would express itself an infinite amount of times

then the TOTAL NUMBER TIMES YOUR RESULT OCCURS IS only 50/∞.

But the likelyhood of equally occuring results is beyond the results of your assumption AND NOT CONSISTENT WITH EXPERIMENTATION. For 6-sided dice, the static probabilities of any one of them resulting in a six-pip is as such:

1 dice 1/6
2 dice 1/8
3 dice 73/648
4 dice 65/648
5 dice 361/3888
6 dice 24017/279936
7 dice 7553/93312

IN WHAT WAY DOES THAT LOOK LIKE ALL RESULTS ARE EVENLY OCCURING?

Furthermore, the more dice you add the LESS even the results, and the less likely a 6 will occur.

If you said 1 dice,.. then yes... mathematically it would apply, and philosophically be sound.

With two you chances of rolling 12 is .025,.. basically 2.5% chance. When if it were even, it would be a little bit more than 8%, right?

If you don't know math is a philosophy INDEED THE ROOT OF PHILOSOPHY, and you want to try engineering a perpetual energy model, or approaching the Cybernetics of Quantum and Chaos theory, you have to get some books on algebra.

How do you propose you are going to "make sure you have enough copper to conduct a current to transform, and not so much as to impede bouyancy? guesswork and assumption, or actual review of experimentation and statistical analysis?

#16

See Yelram,.. here is the percentange chance of any given roll of 5 dice resulting in a score in the game of Yahtzee:

2 of a kind 60.19%
3 of a kind 15.43%
4 of a kind 1.93%
full house 3.86%
sm. straight 12.35%
lg. straight 3.09%
Yahtzee 0.08%

what you are asking for, is that any given roll of twice as many dice result in a "double yahtzee" that are both six-pip.

statistics stand against you that a given number is rolled, if it is more than one dice, and more dice, the less likely a 1 or 6.

furthermore,

statistics stand against an even chance for any given outcome.

what makes you think any infinite number of rolls will affect those low level of probabilities?

BTW:

Yahtzee is the name of the game because it was invented for a rich couple to play on their yacht, and yacht game quicky became "yahtzee". it was a betting game, until released by hasbro.

#17

When you have defined ∞ as the value of the number of repetitions,.. and you further establish that (in your assumption) all of your FIFTY OUTCOMES are EQUALLY REPRESENTED...

as you said:

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If you were to roll dice an infinite amount of times every possible outcome would express itself an infinite amount of times

then the TOTAL NUMBER TIMES YOUR RESULT OCCURS IS only 50/∞.

I completely agree with that. 50/∞=∞ though. So the amount of times it occurs is ∞.

#18

ok, now we are getting somewhere.

what you said is disproven in the oldest writing about the nature of infinity. The Yajur Veda (Offering of Knowledge) is one of the oldest books in existence on mathematics. It mentions "purna", which is translated as "Fullness, or Complete Inifinity." The Yajur Veda documents the earliest known use of numbers as large as parardha (one trillion). It specificaly adresses infinity as such, If you subtract purna from purna, you are still left with purna.

That is much like what you ae saying. A portion of inifinty is the sum of the whole. No portion can be added or taken away that will make it less than infinity.

That is true, but IT DOES NOT say that each of the portions is nessecarily infinity.

50/∞ does not equal ∞.

it only equals 2% of ∞. It stands that that is only a portion, and a relatively small one at that.

for more on the Yajur Veda, visit here: http://www.baghdadmuseum.org/ref/index. ... Yajur_Veda

But see you are not dealing with Infinity, anyways,.. and are using a it as a word not conducive to what you mean.

If you were actually rolling 10 dice INFINITY times,.. then you would also be rolling it <>-23985674(4359847940984609486) times. That is is philosophically impossible. By creating a single repetition of a defined task, you are limited to only a certain portion. without dealing with fractions, negative numbers, irrational numbers, or an other variance,.. you are pretty much limiting yourself to all possible positive integers. That is not called Infinity, that is called the Continuum. This is the infinity of a process, which never stops, and is called potential infinity.

by the way, in the formula x = 50/∞ x is equal to an IRREDUCIBLE POLYNOMIAL,.. and can only be rexpressed in a relation of at least two numbers or variable. In simple terms, the only way you could "solve for ∞, is by multiplying both sides by 50, which renders the statment as 50x = ∞.

just as you can not divide by 0 or -0, you can not divide by any Absolute Number, inclduing ∞

#19

We're going to have to agree to disagree on this one. I was with you until you said "
50/∞ does not equal ∞.

it only equals 2% of ∞. It stands that that is only a portion, and a relatively small one at that.
"

How can you have 2% of infinity? Really explain this to me.

#20

Basically, I think that this is what it boils down to...

If you were rolling an infinite amout of dice...With an infinite amount of sides...You can get an infinite amount of possibilities...

But, the minute you attach a number to it, it ceases to infinity, because true infinity doesn't have a beginning or an end...Like raum suggested, you may be talking about may be a different, or a another definition of infinity...

Your original argument:

"If you rolled 10 dice an infinite amount of times, eventually they would come up all 6s, but this wouldnt happen just once, but an infinite amount of times", To which there was a reply something like "It is possible that you could roll them an infinite amount of times and never come up all 6s". I found this quite a ridiculous idea, being that within infinity all possibilities are represented an infinite amount of times."

Infinity is a transfinite number, and can't be quantified in that way...Like the other person said, there is no guarantee that you can roll 10 dice and get ANY possibility...You could roll them shits a gajillion times, and never see a three...I think that's what's important...In your original scenario, you are almost exclusively dealing with a probablility...