What if I wanted to emulate a 1d(infinite)?

[unseenmage]

How would one go about implementing a die roll where the result was anything from zero to infinite?

My playgroup is curious if such a mechanism could be useful for limiting technically "infinite" repeatable actions in game.

Alternatively, we could assume a cap for any given action. basically realistic practical limits on "infinity". The human swordsman cannot repeat the action infinitely because he'll eventually sleep, starve, age, etc. In essence using RAW numbers to limit potentially "infinite" actions.

But it's that 1d(infinite) concept that really got my curiosity going.

[Captnq]

By definition, any result on a 1d(infinity) would be infinite.

[eggynack]

By definition, any result on a 1d(infinity) would be infinite.
Nah, just the average result. By definition, any result on a 1d(infinity) would not be infinite, because it would presumably be some natural number.

[Deophaun]

By definition, any result on a 1d(infinity) would be infinite.
Yup.

Basically, the probability of any number you could physically write down if given your entire lifetime to do so coming up is 0, because even that generous domain is infinitesimally small compared with the domain of all integers.

[Alent]

I think you'd roll a ball- It's a 0 sided dice, 1 sided dice, or an atomically sided dice depending on how you look at it.

More realistically, uh... roll percentile, go to the next table for values of 100?

[Rakaydos]

If every face was equally likely, the average roll of a D(infinite) is (infinity)/2, which is still infinite.

However it the odds were uneven, you could get a die like:
50% chance of a 1
25% chance of a 2
12.5% chance of a 3
6.25% chance of a 4
3.125% chance of a 6
...ect, all the way to infinity.

[Kazyan]

The result on 1d(infinite) would be arbitrarily high, for a distribution similar to that of regular 1d(whatever). Consider this: pick a number, and compare the chances of rolling lower than that on the d(infinte) to the chance of rolling higher than that.

[Captnq]

Nah, just the average result. By definition, any result on a 1d(infinity) would not be infinite, because it would presumably be some natural number.

You add infinity to 1 for infinity +1 as the total number of possible results. To get the average result you divide by 2. (Infinity+1)/2 is infinity. So the result of 1d(infinity) is infinity.

[eggynack]

You add infinity to 1 for infinity +1 as the total number of possible results. To get the average result you divide by 2. (Infinity+1)/2 is infinity. So the result of 1d(infinity) is infinity.
The average result isn't the same as any given instantiated result. The former is infinite, and the latter isn't, which is what I said. A roll of 1d(infinity) could yield 17,000,412, or it could yield 7, or it could yield the width of the known universe in centimeters. The one thing it won't yield, and indeed can never yield, is a result of infinity. Because infinity isn't a number.

[Fax Celestis]

Do you really need infinite or can you get away with arbitrarily high?

It's pretty easy to emulate a d100000, for instance.

[KillianHawkeye]

As the number of sides approaches infinity, the probability of rolling any given number approaches zero. Therefore, a d∞, once thrown, would never stop rolling. Congratulations, you've invented perpetual motion!




infinity isn't a number.

Correction: infinity isn't a finite number.

[Deophaun]

The average result isn't the same as any given instantiated result. The former is infinite, and the latter isn't, which is what I said. A roll of 1d(infinity) could yield 17,000,412, or it could yield 7, or it could yield the width of the known universe in centimeters.
Probability says it will never yield a number that can be contained by the universe.

The one thing it won't yield, and indeed can never yield, is a result of infinity. Because infinity isn't a number.
True. The correct term was used by Kazyan: "arbitrarily high." But considering there's no arbitrator who could ever express such a number, "infinity" is practically correct.

[Particle_Man]

Getting away from theory for a second, here's something that 2nd ed AD&D did for the damage for firearms and that Savage Worlds and Earthdawn did for practically everything: Exploding dice.

Say you roll a d8. If you get 1 to 7 stop. If you get 8, then roll it again, adding 8 to the result. If you get 1 to 7 stop. If you get 8, roll it again, adding another 8 to the result. Repeat until you stop.

Technically this could mean you roll forever. In practical terms you won't. So this is sorta 1d(infinity) except obviously there is a higher probability for getting lower numbers, like 5, than higher ones, like 103.

Would that give you what you wanted?

[Edit: this doesn't just apply to d8. You could apply it to any finite die type, really]

[eggynack]

Correction: infinity isn't a finite number.
I'm pretty sure my statement was the correct one. It's just not a number.

Probability says it will never yield a number that can be contained by the universe.
Probability says that it will never yield any number within any given range of values, but yield one it will, unless you're going with the perpetual motion die.


True. The correct term was used by Kazyan: "arbitrarily high." But considering there's no arbitrator who could ever express such a number, "infinity" is practically correct.
Pretty much, though practically correct and actually correct are two really different things where infinity is concerned.

[Deophaun]

Pretty much, though practically correct and actually correct are two really different things where infinity is concerned.
If you're multiplying and dividing infinities by each other, sure. But for the purposes of the 1dinfinity as defined by the OP? The outcomes are identical.

[Captnq]

The average result isn't the same as any given instantiated result. The former is infinite, and the latter isn't, which is what I said. A roll of 1d(infinity) could yield 17,000,412, or it could yield 7, or it could yield the width of the known universe in centimeters. The one thing it won't yield, and indeed can never yield, is a result of infinity. Because infinity isn't a number.

If it can't yield the highest result, then it isn't a 1d(infinity) die.

If I had a 1d11, but it couldn't roll an 11, only one to ten, could I claim it to be a 1d11? No. You are telling me, you have a 1d(Infinity) die, but it can't actually roll infinity, so it rolls some number that isn't infinite, but it's still an 1d(Infinity) die? What???

It either is infinite, or it's not. If you say it's not infinite, then it's not a 1d(infinity) die and we are talking about two different dice.

The die I am talking about is 1d(infinity). I don't know what 1d(whatever) die you're talking about.

[Fax Celestis]

Getting away from theory for a second, here's something that 2nd ed AD&D did for the damage for firearms and that Savage Worlds and Earthdawn did for practically everything: Exploding dice.

Say you roll a d8. If you get 1 to 7 stop. If you get 8, then roll it again, adding 8 to the result. If you get 1 to 7 stop. If you get 8, roll it again, adding another 8 to the result. Repeat until you stop.

Technically this could mean you roll forever. In practical terms you won't. So this is sorta 1d(infinity) except obviously there is a higher probability for getting lower numbers, like 5, than higher ones, like 103.

Would that give you what you wanted?

[Edit: this doesn't just apply to d8. You could apply it to any finite die type, really]

The issue with exploding dice is they make an inverse exponential curve (the higher the result, the lower the chance of rolling it on an exponential scale). Multiple dice make bell curves (at least when grouping them), whereas something like a d800 has a linear probability "curve" (all sides have the same odds). I mean, sure, exploding dice sure can theoretically reach arbitrarily high values, but not at the same probability per face.

Not that 1/infinity is much of a probability to work with, but still.

[eggynack]

If it can't yield the highest result, then it isn't a 1d(infinity) die.
It can't yield the highest result, because yielding infinity is meaningless. That's part of the reason why this doesn't make much sense.

Edit: Presumably, a d(infinity) would just yield some natural number, selected arbitrarily from the set of all natural numbers.

[Slipperychicken]

Exploding dice systems like Shadowrun generate numbers without an upper bound, but on a sort-of-normal/bell-shaped curve. It wouldn't get the even distribution you would expect from a 1d(infinity).


How would one go about implementing a die roll where the result was anything from zero to infinite?


By the power of undergrad-level statistics...

1. Infinity isn't a number, just the state of being unbounded (i.e. not finite).

2. Every result of such a function would have 0% probability, but still be possible (just like in a continuous distribution).

3. No amount of storage could contain the highest result, partly because there is no highest result. The 1d(infinity) would not be possible due to technical constraints.

[tzar1990]

I'm pretty sure my statement was the correct one. It's just not a number.

Probability says that it will never yield any number within any given range of values, but yield one it will, unless you're going with the perpetual motion die.


Pretty much, though practically correct and actually correct are two really different things where infinity is concerned.

Fine, it will yield any given number given an infinite amount of time.

However, the odds of it rolling any number, or any member of a finite set of numbers, is 0.

That is to say, yes, it could theoretically roll a 7. But there are an infinite number of non-7 integers, so the odds of rolling that 7 approach zero as the number of sides on the dice approaches infinity.

Similarily, for any finite set of numbers, there are infinitely more numbers that are excluded from it, and as such the odds of a member of that set being chosen is zero.

Unfortunately for OP, the "set of all integers which can be expressed in any way, shape or form known to mankind" is ludicrously huge, but still finite - there are numbers out there so ludicrously big you would need to invent your own new notation system just to express them. And if you're attempting to use a d-Infinity, then you'll swiftly realize that the set of those uselessly enormous numbers is non-finite, as it consists of everything above a certain point. As such, the odds of getting a uselessly huge number approaches one.

[Captnq]

It can't yield the highest result, because yielding infinity is meaningless. That's part of the reason why this doesn't make much sense.

Edit: Presumably, a d(infinity) would just yield some natural number, selected arbitrarily from the set of all natural numbers.

Just because it's meaningless doesn't mean it stops following the rules of mathematics.
1d(infinity) yields infinity. Period. End of statement. It cannot exist in the real world, true, but that has nothing to do with math. Dragons don't exist and you don't have problems playing a game named after them. Why do you have the problem dealing with a change to the fundimental laws of the universe that considers the possibility that infinity exists and what possible outcomes would result from that?

The question asks "How would one go about implementing a die roll where the result was anything from zero to infinite?"

The answer? You can't.

Any result from a 1d(infinity) die would be infinite. The only way to get any other result is to ignore the original question and change the assumptions the question is built upon.

You can't just ignore the OP and make up your own rules and say "This is what will happen."

[eggynack]

Just because it's meaningless doesn't mean it stops following the rules of mathematics.
I'm saying that it does. You just can't yield infinity, because it's a non-object. You can approach infinity, and you can consider infinite things, but it's not a number, and it can't exist on any die, including a theoretical one.

[Slipperychicken]

Any result from a 1d(infinity) die would be infinite.

You could totally roll a natural 1, it just has 0% probability.

[Captnq]

I'm saying that it does. You just can't yield infinity, because it's a non-object. You can approach infinity, and you can consider infinite things, but it's not a number, and it can't exist on any die, including a theoretical one.

Correct. Because any die that was 1d(infinity) would always result in infinity every time you rolled it. You might as well have a perfect sphere that reads, "INFINITY"

It will NEVER result in a number.

[unseenmage]

Okay, so 1d(infinity) is a largely useless concept. Got it.
And thanks.

What about a 1d(maximum)? Assume that every situation can be solved with enough sides of the die. The number of sides is variable from situation to situation.

What about that? Is there a potential way to implement that?

[Captnq]

You could totally roll a natural 1, it just has 0% probability.

No. That's not how infinity works.

If you assume the possibility of a 1d(infinity) die, it must always result in infinity. Stop trying to impose reality on an impossible situation. The question itself requires you IGNORE HOW REALITY WORKS.

To assume that a 1d(infinity) die exists requires that you throw out reality. When we test out theoretical die, it always will result in infinity. Always. Period. Never anything else.

You keep trying to apply "common sense" to something that is a question where reality no longer applies. There are new rules. Here is the new rule for this THEORETICAL question:

Infinity is possible.

Then you test the theory.

The test results in something that cannot happen.

The answer to the question is: Nope. You can't do it.

Now, everyone agrees to the last part, it's not possible, but you are all screwing up step 3. You keep saying the die will result in a possible number. It can't. There will never be a possible number on that die, EVER. Infinity WINS. There is no infinity + 1, nothing just short of infinity, there is just infinity. No result on that die will ever be anything else, other than INFINITY. That's what infinity MEANS.

[Deophaun]

What about a 1d(maximum)? Assume that every situation can be solved with enough sides of the die. The number of sides is variable from situation to situation.

What about that? Is there a potential way to implement that?
Not entirely sure what you mean by that, but the forum's die roller should be able to do, say, 1d2573292, if that's what you're after. Of course, at that point, you might be better off just using a percentile.

[Captnq]

Okay, so 1d(infinity) is a largely useless concept. Got it.
And thanks.

What about a 1d(maximum)? Assume that every situation can be solved with enough sides of the die. The number of sides is variable from situation to situation.

What about that? Is there a potential way to implement that?

Oh yeah. It's called Crystal Ball. I highly recommend it. Program in all sorts of custom dice combinations. I use it for everything.

[Doc_Maynot]

You just can't cook with petrol when it comes to infinity.

I mean seriously? The sum off all numbers from 1 to infinity is -1/12 (http://www.youtube.com/watch?v=w-I6XTVZXww)

[JusticeZero]

Alternately, use exploding percentile dice to make a curve between 0 and 1. If your tens comes up 0 or 9, shift the ones over one decimal place and roll another d10. If it's the same, repeat, until you have numbers that curve like..
0.0000036
0.00010
0.0093
0.061
0.52
0.87
0.928
0.9989
0.9999951

[Slipperychicken]

If you assume the possibility of a 1d(infinity) die, it must always result in infinity.

Can you prove this?



Now, everyone agrees to the last part, it's not possible, but you are all screwing up step 3. You keep saying the die will result in a possible number. It can't. There will never be a possible number on that die, EVER. Infinity WINS. There is no infinity + 1, nothing just short of infinity, there is just infinity. No result on that die will ever be anything else, other than INFINITY. That's what infinity MEANS.

As I understand it, the set of possible values (as would be defined by an infinity-sided die) is all integers greater than or equal to 1 (i.e. X>=1). That set includes the number 1.

[Deophaun]

Now, everyone agrees to the last part, it's not possible, but you are all screwing up step 3. You keep saying the die will result in a possible number. It can't. There will never be a possible number on that die, EVER. Infinity WINS. There is no infinity + 1, nothing just short of infinity, there is just infinity. No result on that die will ever be anything else, other than INFINITY. That's what infinity MEANS.
The problem is you're confusing "finite" with "possible," and the two aren't the same. The number itself may not be possible, but that doesn't mean it isn't a real integer. The number will just be inexpressible, which, for our purposes, means you're right and we might as well treat it as infinity. So 10,000/(1dinfinity) = 0.

However, beyond our purposes here, you can't treat it as infinity. If you did an equation like infinity/(1dinfinity), you would wind up with infinity, and not 1, because the results of 1dinfinity will result in a finite number despite its inexpressibility.

[JusticeZero]

While it contains 1, the number of rolls needed, on average, to find a result within that range that has less digits than the number of atoms contained within the universe is infinitely longer than will happen during the age of the universe, assuming that every subatomic particle rolled said dice once every picosecond from the Big Bang on.

[Sith_Happens]

I mean seriously? The sum off all numbers from 1 to infinity is -1/12 (http://www.youtube.com/watch?v=w-I6XTVZXww)

Someone needs to slap the guy in that video for making it sound like what he did with S1 was actually an arithmetic sum, as opposed to an obscure number theory technique that physicists use when they have to pretend that a divergent series has a sum.

So no, the sum of all positive integers is not -1/12, it very much is infinity. -1/12 is just the value you use when a weird physics problem forces you to ignore actual series math.

[nyjastul69]

You just can't cook with petrol when it comes to infinity.

I mean seriously? The sum off all numbers from 1 to infinity is -1/12 (http://www.youtube.com/watch?v=w-I6XTVZXww)

This (http://scientopia.org/blogs/goodmath/2014/01/17/bad-math-from-the-bad-astronomer/) explains where he went wrong.

[Deophaun]

Someone needs to slap the guy in that video for making it sound like what he did with S1 was actually an arithmetic sum, as opposed to an obscure number theory technique that physicists use when they have to pretend that a divergent series has a sum.
I'm not a math guy, but I got the distinct feeling that trick was like dividing by zero to show 2+2=5.

[Zweisteine]

If you assume the possibility of a 1d(infinity) die, it must always result in infinity. Stop trying to impose reality on an impossible situation. The question itself requires you IGNORE HOW REALITY WORKS.I can't tell how serious you're being. You are, certainly, taking Slipperychickens "0% probability of a 1 comment far too seriously, I think.
May I make a suggestion?
Yes? Okay.
I believe that the question does not mean for a die going from one to the "virtual number" called infinity. I believe that the question is asking about a die that can roll any counting number.

The average roll for such a die would be infinitely high, but it would not be "infinity," as "infinity" is not a number. (Though I suppose that these could be the same, depending on what you consider "infinite" to mean (Yes, I know it's not really subjective, but many things that shouldn't be are, to some small degree)).


I believe that the probability of rolling a 1 (or any given number) on a d(infinity) would be something like this:

_
0.01%

[Slipperychicken]

While it contains 1, the number of rolls needed, on average, to find a result within that range that has less digits than the number of atoms contained within the universe is infinitely longer than will happen during the age of the universe, assuming that every subatomic particle rolled said dice once every picosecond from the Big Bang on.

How can one say for sure how many trials it will take to get a given outcome through random number generation? (granted, one can generally estimate it with some certainty, but not 100%) As I understand random generation, you might get a given outcome in the first go, and you might never get it.

[Deophaun]

How can one say for sure how many trials it will take to get a given outcome through random number generation? (granted, one can generally estimate it with some certainty, but not 100%)
We're dealing with infinity, which results in some very strange math. For example, the percentage of all numbers that contain the number "3" is 100%, even though we know 1, 2, 4, 5, 6, 7, 8, and 9 exist. So essentially it is a 100% certainty that you will never get a useable number out of 1dinfinity.

[fryplink]

Not much of a math person myself (I took Stats for my undergrad math credit). In those weird situations where repeating loops appropriately occur (IE: when most of the table thinks the effect is acceptable; when they don't we just undo the action and let them rebuild at the end of the session), we (those at our table) have a solution. If you can optionally cease the loop, you must choose a real number, although it can be arbitrarily high. The number of atoms in a gram of hydrogen is the one we typically use (I believe this is called one mole). If the loop is self creating with no outlet, every value is treated as sufficient to completing it's task, but has no leftovers, unless the effect specifically spells out the effects of numeric leftovers. If it does specify it's leftovers (like protection from arrows does), it's value is also treated as enough for the task at hand. This continues until the ultimate conclusion is obvious for the majority of people at the table as well as anyone directly effected.

For example, Superboy (1d2 crusader) is treated as dealing "just enough" damage, since you can't leave the combo. If you were able to leave the combo (I'm coming up blank currently), we require the player to choose an actual number, which is often 6.02214129(27)×(10^23). This has only ever once actually been an important distinction (and it was in Paranoia thankfully, where someone tried to infinitely eat (they had to choose an amount, but it could be any amount)an (actual) infinite source of energy.

Yes, I know it's a house-rule, and in competitive table top situations we limit infinite combos to 25 or 256 iterations depending on an attendance-based vote. I'm sharing this because I don't think working the math of the situation is going to solve your "problem". I think setting up a rule handle these situations is what you need.

For your situation (where you have to find a random number between 1 and yes), my table would ask if the origin of the effect can put a ceiling on the effect? If they can (I recognize it's not truly infinite at this point), we'd have them do so and then generate a number from that (most would be bright enough to choose one in massive excess of what they need). If they can't put a ceiling on it, we would treat it like superboy, acting as if they always had ''just enough" to accomplish what the effect is aiming to accomplish.

[Hand_of_Vecna]

You would have a NI (as in infinite over non infinite) chance of getting an arbitrarily high number and by arbitrarily high I mean numbers ove googol to the googol power or any other higher number you can imagine.

[Jack_Simth]

Okay, so 1d(infinity) is a largely useless concept. Got it.
And thanks.

What about a 1d(maximum)? Assume that every situation can be solved with enough sides of the die. The number of sides is variable from situation to situation.

What about that? Is there a potential way to implement that?
Sure. You just need an arbitrary roller (like what you have on the forums). Highest = (DC - bonus). If you have a +12 modifier, and you're rolling against DC 20, you use a d8. If you have a +12 modifier, and you're rolling against DC 100, you use a d88. If you have a +12 modifier, and you're rolling against DC 1000, you use a d988. And so on.

[Kraken]

For what it's worth, Excel (and presumably other spreadsheet programs) can do arbitrarily large random numbers, presumably up to a limit of some sort. Using Excel 2007, =RANDBETWEEN(1,999999999999999) spits out a random number with those minimum and maximum values. If you go any higher it starts rounding. For instance, =RANDBETWEEN(1,9.99999999999999E+150) will spit out enormous random numbers, but here's the first ten results to show the effects of rounding.

4,802,866,986,100,460,000,000,000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000

5,470,964,173,842,450,000,000,000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000

7,426,132,397,774,820,000,000,000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000

8,251,889,924,206,090,000,000,000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000

4,755,536,461,008,290,000,000,000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000

574,463,655,631,716,000,000,000,000,000,000,000,00 0,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000

6,305,405,311,446,080,000,000,000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000

7,663,207,080,015,390,000,000,000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000

1,965,263,397,668,070,000,000,000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000

3,354,192,124,417,040,000,000,000,000,000,000,000, 000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,00 0,000,000,000

[Sith_Happens]

For example, the percentage of all numbers that contain the number "3" is 100%, even though we know 1, 2, 4, 5, 6, 7, 8, and 9 exist.

I know just enough about set theory to say that this is incorrect. Certain infinite sets can be "bigger" than others (for example, there are more integers than even integers), at least sometimes to the point that an exact size ratio can be determined.

[Deophaun]

I know just enough about set theory to say that this is incorrect. Certain infinite sets can be "bigger" than others (for example, there are more integers than even integers), at least sometimes to the point that an exact size ratio can be determined.
No, it's very much correct. As there is a 10% chance that any place value in a number will be 3, we are left with a formula that looks like this:

100 * (1 - (9/10)^infinity). (9/10)^infinity = 0, so that's 100 * (1-0), or 100%.

Meanwhile, if you're looking at the number of even integers, you're basically just looking at the last place, and the other place values make no difference. Since half of those values will be divisible by 2 (except in the case of the number "0"), you get 100 * (1 - (5/10)), or 50% of the infinite series being even.

[Irk]

Someone needs to slap the guy in that video for making it sound like what he did with S1 was actually an arithmetic sum, as opposed to an obscure number theory technique that physicists use when they have to pretend that a divergent series has a sum.
I know enough about this sort of thing to agree with you, that's not how sums work, but I am curious in what scenario the 'obscure number theory technique' (taking the average of the value of the sum after an even and odd number of terms) applies.

[TuggyNE]

So essentially it is a 100% certainty that you will never get a useable number out of 1dinfinity.

If you roll 1d∞, you will get some definite result from the set of natural numbers, although it may be so absurdly high as to be inexpressible with Graham's notation or similar written across the entire universe. You won't get "infinity", and there is always some tiny chance of getting a 1, or a 20, or any other number, although that probability is so small as to be inexpressible as anything other than 1/∞.

[Lostbutseeking]

I know just enough about set theory to say that this is incorrect. Certain infinite sets can be "bigger" than others (for example, there are more integers than even integers), at least sometimes to the point that an exact size ratio can be determined.

Georg Cantor would disagree. There are exactly as many even natural numbers as there are natural numbers.

And the brutal torture of mathematics in this thread makes me weep.

[eggynack]

Georg Cantor would disagree. There are exactly as many even natural numbers as there are natural numbers.

Indeed. There are larger infinite sets though. For example, the set of all real numbers is greater than the set of all integers.

[Deophaun]

If you roll 1d∞, you will get some definite result from the set of natural numbers, although it may be so absurdly high as to be inexpressible with Graham's notation or similar written across the entire universe.
Which would be an unusable number, would it not?

If you are going to agree with me, I would prefer it if you did not phrase your response as a disagreement.

[Larkas]

You can't roll a d∞ simply because ∞ isn't a number. Seriously, you can't have a die with ∞ faces. I was going to say that the best you could hope for is a dlim->∞, but that doesn't make much sense or is useful in any form.

Eh, unless you're rolling for stuff in the Far Realm. Then go crazy rolling your d∞.

[Phelix-Mu]

Every time someone posts in this thread, whether it be stunning mathematical analysis or less so, an angel gets its wings.

Seriously, we need more of this kind of thing.:smallsmile:

[unseenmage]

Every time someone posts in this thread, whether it be stunning mathematical analysis or less so, an angel gets its wings.

Seriously, we need more of this kind of thing.:smallsmile:

Ladies and gentlemen we have a winner.
One Phelix-Mu managed to make me laugh hard enough through my cold that I coughed hard enough to have trouble breathing.

Congratulations, my dinner won't sit right for the rest of the evening. :smallbiggrin:

[Jeff the Green]

[SIZE="1"]I believe that the probability of rolling a 1 (or any given number) on a d(infinity) would be something like this:

_
0.01%

Which is equal to 0%, in much the same way that 0.999... = 1.

[SowZ]

You may as well divide Margaret Thatcher's resignation by a potato. The result will be equally sensible.

[Drachasor]

Roll a d10. That's the first digit on the far right.
Roll a d10. That's the second digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.
Roll a d10. That's the next digit on the far right.

Keep going on like that. I'm sure you'll get there eventually.

Note, the chance of getting 1 isn't different than the chance of getting 100, or 1445234524 or any other finite number. At some point all future rolls need to be 0s, which is for all intents and purposes impossible.

[weckar]

Actually, Drachasor... There is no '0' on a regulation d10. It runs 1-10.

[Deophaun]

Actually, Drachasor... There is no '0' on a regulation d10. It runs 1-10.
There's a "regulation" d10? Regulated by who?

[weckar]

Used to be RPGA that did that. Not sure about now.

[Drachasor]

Actually, Drachasor... There is no '0' on a regulation d10. It runs 1-10.

Your point?

If you have a d10 that shows a '10' and not a '0' then treat the '10' as a zero.

Obviously.

Edit: You could use any sided die you want for this really. A d6 would do it in base 6, a d8 in base 8, a d20 in base 20.

[weckar]

I'm Sorry, I figured this thread had lost the need for 'points' a while ago.

[Deophaun]

Used to be RPGA that did that. Not sure about now.
The RPGA document doesn't lay out what is a "regulation" die. And most d10s I've come across are of the 0-9 variety, mainly because they double as percentiles.

[weckar]

Most percentile tables run 1-100 instead of 0-99 for a reason :smallwink:

[Deophaun]

Most percentile tables run 1-100 instead of 0-99 for a reason :smallwink:
Actually, if I'm not mistaken, I think the old AD&D tables were 00-99. I did have a d100 that ran that way.

Anyway, you'll find percentile dice have one that's 0-9, and another that's 00-90. 100 is 00 0.

[weckar]

I own at least 80 sets of percentile dice, and I can honestly say I have never seen that. Then again, I do not own ALL sets, so I'll regard your claim as valid.

[Sith_Happens]

I know enough about this sort of thing to agree with you, that's not how sums work, but I am curious in what scenario the 'obscure number theory technique' (taking the average of the value of the sum after an even and odd number of terms) applies.

In string theory, apparently.

[prufock]

It's completely pointless. A die has a 1/# of faces chance of returning each result. 1/infinity is undefined, so there is no calculation to determine how likely any one result is. The limit approaches 0, and a 0% chance of each result isn't very useful.

[Hand_of_Vecna]

Most percentile tables run 1-100 instead of 0-99 for a reason :smallwink:

Yes, but treating 00 as 100 is the exception not the rule. If the top number was 10 rather then 1 you'd get 100 by rolling a 90 and a 10 and the chart would run from 11-120.

[Particle_Man]

Okay, so 1d(infinity) is a largely useless concept. Got it.
And thanks.

What about a 1d(maximum)? Assume that every situation can be solved with enough sides of the die. The number of sides is variable from situation to situation.

What about that? Is there a potential way to implement that?

This might lead to a curious result.

If you applied it to pc damage rolls and set the maximum to something like the npc opponent's hp (assuming at at 0 hp the opponent goes down, which is not RAW but does save time, especially for this example). So with an opponent with 244 hp, the roll of d244 gets you, say 142. Then the opponent has 102 hp, so you roll d102 and get, say, 50. Then you roll d52 on the third successful hit, and get, say 48. Now the opponent has 4 hp, so your 4th successful hit rolls d4. Then you get 3 so your next successful hit rolls d1, which is enough to take the opponent down.

Is that the effect you are looking for?

[unseenmage]

This might lead to a curious result.

If you applied it to pc damage rolls and set the maximum to something like the npc opponent's hp (assuming at at 0 hp the opponent goes down, which is not RAW but does save time, especially for this example). So with an opponent with 244 hp, the roll of d244 gets you, say 142. Then the opponent has 102 hp, so you roll d102 and get, say, 50. Then you roll d52 on the third successful hit, and get, say 48. Now the opponent has 4 hp, so your 4th successful hit rolls d4. Then you get 3 so your next successful hit rolls d1, which is enough to take the opponent down.

Is that the effect you are looking for?

That sounds about right.
Too bad it's so unwieldy to implement without computerized assistance.

[Drachasor]

Okay, so 1d(infinity) is a largely useless concept. Got it.
And thanks.

What about a 1d(maximum)? Assume that every situation can be solved with enough sides of the die. The number of sides is variable from situation to situation.

What about that? Is there a potential way to implement that?

This is not hard to do. Let's say you have a number
ABCD, where each letter represents a digit 0-9.

For the left-most digit, use the smallest die that's bigger than that digit (so a d2 for a 1, a d4 for a 2 or 3, a d6 for a 4 or 5, etc). For all other digits use a d10. Reroll any digits that are too high if you go over. Note, that the largest number on any die should be treated as a zero.

So for 3789, roll a d4, d10, d10, d10.

If you get a 4 on the d4, reroll the d4.
If you get a 3 on on the d4, and an 8 or a 9 on the first d10, reroll that d10.
If you get a 3 on the d4, a 7 on the first d10, and a 9 on the next d10, reroll that d10.

That's probably the easiest way to do it and calculate the result. There are ways to do it with far fewer potential rerolls, but you end up spending more time calculating.

Another option with fewer rerolls though, would be to roll each digit one at a time. Then you pick the smallest die for the next digit that's bigger than the allowed numbers. If all the next numbers can be d10s, then just use them.

So if you had a 4325, then you'd first roll a d6, rerolling if you get a 5.
If you roll a 1, 2, 3, or 6, then you roll d1000 for the next 3 digits.
If you roll a 4, then you need to roll a d4 for the 3rd digit. If you roll a 2 on that d4, then you roll a d6 for the last digit. This can be quicker if you have a lot of lower numbers.

That or use a computer/calculator.


Yes, but treating 00 as 100 is the exception not the rule. If the top number was 10 rather then 1 you'd get 100 by rolling a 90 and a 10 and the chart would run from 11-120.

11-110, you mean.

[Kraken]

Yes, but treating 00 as 100 is the exception not the rule. If the top number was 10 rather then 1 you'd get 100 by rolling a 90 and a 10 and the chart would run from 11-120.





11-110, you mean.

What? If I'm following this correctly, 00 and 1 would be 1, 00 and 10 would be 10, and 10 and 10 would be 20. Which results in a range of 1-100, without needing to make the 0 and 00 = 100 exception.

[Drachasor]

What? If I'm following this correctly, 00 and 1 would be 1, 00 and 10 would be 10, and 10 and 10 would be 20. Which results in a range of 1-100, without needing to make the 0 and 00 = 100 exception.

If you treat all the d10s as going from 1-10, then using two d10s for a d100 gets you 11-110 (a 0 on both dice is 10*10 + 10, and a 10 on one die and the 1 on the other die is 10*10 + 1 = 101, and a 1 on both dice is 1*10 + 1 = 11). Similarly, you get a 100 by rolling a 9 and a 0, since 9*10 + 10 = 100.

If you treat both dice as being a zero, when they roll 0, then you get Zero-99.

We normally treat them both as zero when your roll a 0. The exception being if you roll 00, in which case the first d10 is treated as a 10. Basically. It's not treated as a 10 otherwise, and the other die is never treated as a 10.

[Kraken]

Ah, my mistake, I thought this conversation assumed the 0-9 dice was being changed to 1-10, and the 00 on the second d10 would be treated as 0.

[Svata]

You can't roll a d∞ simply because ∞ isn't a number. Seriously, you can't have a die with ∞ faces. I was going to say that the best you could hope for is a dlim->∞, but that doesn't make much sense or is useful in any form.

Eh, unless you're rolling for stuff in the Far Realm. Then go crazy rolling your d∞.

Roll 1dInfinity in the far realm amd you'll probably get a result of »§№£»

[Particle_Man]

That sounds about right.
Too bad it's so unwieldy to implement without computerized assistance.

In the particular example I gave, that would mean that a dagger does the same amount of damage on a specific attack on a specific opponent as a greatsword. Which is interesting (a shout-out to OD&D in a way), as long as that is what you are looking for.

[veti]

What about a 1d(maximum)? Assume that every situation can be solved with enough sides of the die. The number of sides is variable from situation to situation.

What about that? Is there a potential way to implement that?

That's easy. Same as you roll 2d10 to get a result from 1 to 100, so 3d10 will give you 1 to 1000, 4d10 1 to 10,000, etc. Let's say you've got 6d10 in total - that will give you a d(million) on the first roll. That's the first six digits of your result, then roll them again to get the next six digits, and so on.

There's no limit to how much precision you can get in your answer, if you really care about it. I'm finding it really hard to imagine a situation in which that would be useful, though.

[Snowbluff]

If it's for a damage die, you can just say whatever got hit died. The odds of a target surviving a hit are infinitesimally small, whatever it's HP is. That's assuming is has a plausible HP, of course.

If I were to even start making up a number I pretended to roll on a d(inifity), I would roll all of my die, and multiply them for the number of digits, then roll a d10 for each digit.

[Irk]

In string theory, apparently.I checked on Wikipedia, and it says that they are not sums "in the traditional sense", because they use weird techniques to assign values to divergent series. Furthermore, Wikipedia also says that such sums are useful in only very specific fields such as complex analysis, quantum field theory, and of course, string theory. None of those really seem to be part of standard Riemann sums, at least not in the way I was taught, so its really just some stupid mathematical trickery that only matters when your screwing around with really complex and very situational mathematics.

[Chronos]

All of mathematics is just trickery, some of which happens to be occasionally relevant to the real world. The sum of all natural numbers being -1/12 is no less "true" or "real" than the sum of all reciprocal squared natural numbers being pi^2/6.

And when we refer to a dn, we usually mean a draw from a uniform distribution of integers from 1 to n. By this standard, a dinfinity would be expected to mean a draw from a uniform distribution on the positive integers. But there is no such distribution. You can have a uniform distribution on the reals in some finite interval, but you cannot have a uniform distribution on a set of countably-infinite size. If you want a nonzero distribution on all the positive integers, you can have that, but it won't be uniform, and you'll need to specify just how you want it to be nonuniform.

[Irk]

no less "true" or "real" than the sum of all reciprocal squared natural numbers being pi^2/6.
Well, I dunno, can you prove this with obscure mathematical techniques? (It is possible you just mentioned a variation of the -1/12 thing of which I am unaware, in which case I'm incorrect.)

[Larkas]

Roll 1dInfinity in the far realm amd you'll probably get a result of »§№£»

Either that, or mashed potatoes.

[Fortuna]

I just want to note that people are talking about a dinfinity, or even a lim n->infinity dn, as though such a concept is meaningful. It turns out not to be, at least not with conventional notions of probability and number - you need to get into middling-sophisticated mathematics to develop the notions you need to express such a concept meaningfully in any kind of rigorous way. The problem arises from the principle of unitarity - that is, the principle that the sum of the probabilities of all possibilities should equal one. A die is generally understood to produce a uniform discrete distribution - that is to say, every number that can be rolled has an equal probability to be rolled. The problem is that there is no real number which that probability can be for a dinfinity, because for any number greater than zero, the sum of probabilities will be infinite, and for zero, the sum of probabilities will be zero. To meaningfully describe a dinfinity, you need to assign each number an infinitesimal probability, which means stepping out of the real numbers and into the superreals or some related family.

Now, that said, it is possible to create meaningful distributions with arbitrarily long tails, even infinitely long tails - one was suggested way back on the first page, exploding dice. But provably, for large enough numbers the probability of a given number being generated must fall off (since the sum of probabilities must converge to zero).

As to a d(maximum), the simplest approach in my view is to pick the next number you can easily see is the product of 2a+3b+5c and break it down into a product of 4, 6, 8, 10, 12 and 20, then use the dice on hand to generate a random number up to there. If you get a number above your maximum, reroll. This does depend on being quick at mental multiplication and finding factors, though, so you may want to use some other method. Drachasor suggests one with a good underlying notion, although the implementation is a bit faulty (it doesn't allow for numbers in the range 0-10floor(log(maximum)), and has inflated probabilities for numbers near the top of the range - but that's easy enough to fix).

[Sith_Happens]

The sum of all natural numbers being -1/12 is no less "true" or "real" than the sum of all reciprocal squared natural numbers being pi^2/6.

It is in fact less true, because the latter of those is an actual sum while the former is the result of a completely different operation that's merely sometimes referred to as a "sum" because it serves a similar purpose in the select problems to which it applies.

[zottel]

Comming back to the original question...

As many posters have pointed out a "classic" 1d(inf) is not meaningful. In the sense of a classic die giving equal probabilities for any number in its range.

You could however create a die that can give an arbitrary high result with a finite probability. Even with an infinite average.

Here is a "simple" example of a procedure:
You start with one, than you toss a coin.
Heads=break
Tail=multiply by two, toss again.
So throwing the coin and getting lets say: Tail, Tail, Tail, Head gives you 1x2x2x2=8
(this way you can only get integer powers of two, but that gap can be filled easily...)
Now the fun fact of that procedure:
Similar two the "exploding dice" you can get arbitrary high numbers.
But Furthermore, your AVERAGE is also +infinity ;)

But still you have a finite chance to fail a dc of lets say 20 (actually the probability to fail a dc 20 would be 1-0.5^5 approx 97%).

Sidenote: If you want computer program that gives any number between 0 and infinity, with average=infinity, but is still "usable", you could draw a number from a Levy distribution (and cast to int).
https://en.wikipedia.org/wiki/Lévy_distribution


Have fun with math :smallbiggrin:
Zottel

[broodax]

All of mathematics is just trickery, some of which happens to be occasionally relevant to the real world. The sum of all natural numbers being -1/12 is no less "true" or "real" than the sum of all reciprocal squared natural numbers being pi^2/6.

And when we refer to a dn, we usually mean a draw from a uniform distribution of integers from 1 to n. By this standard, a dinfinity would be expected to mean a draw from a uniform distribution on the positive integers. But there is no such distribution. You can have a uniform distribution on the reals in some finite interval, but you cannot have a uniform distribution on a set of countably-infinite size. If you want a nonzero distribution on all the positive integers, you can have that, but it won't be uniform, and you'll need to specify just how you want it to be nonuniform.

Thank you. So, this is the heart of the problem, and the potential solution.

If you define rolling "dice" as giving you a uniform distribution of results, then it is impossible to roll an infinite sided dice. If you throw out the requirement of uniformity, though, it is possible.

You need to have a non-uniform distribution, and you need to define it. We already have a practical dice-based method of doing this as well - exploding dice.

So, a couple options for generating random numbers among all natural numbers:

1) Start with expanded-exploding dice. I.e. roll 1dx and re-roll any number other than 1. Rolling a standard 1d100 in this way would likely get you some somewhat large numbers (relative to "normal" dnd dice results). But, you only have a 1% chance of getting a number higher than 23,358. So this is probably not high enough for your needs.

2) Roll dice for each digit or set of digits of a number. As soon as you roll some value x times in a row, discard x-1 of these and stop rolling. Rolling 1d10 and setting x to 2 would give you a 1% chance of getting something as high as 10^43 or 10^45, which is pretty darn big.

The problem with both of these methods is that they make it rather likely to get extremely low numbers compared to what you'd want. And they can require you to count a maximum result on a 1d100 or 1d10 as zero if you want every natural number to be a possible outcome. But you can tweak this. For instance, in 1) above, you could require y rolls before allowing stopping. In 2) you could start with x=some large number and reduce it by 1 each time you roll.

[Drachasor]

All of mathematics is just trickery, some of which happens to be occasionally relevant to the real world. The sum of all natural numbers being -1/12 is no less "true" or "real" than the sum of all reciprocal squared natural numbers being pi^2/6.

This is just plain false.

First, the sum of all natural numbers does not add up to -1/12. The "proofs" of this rely on a lot of blatantly wrong "math."

On the other hand, the sum of the reciprocal of squared natural numbers does have a fixed value of (pi^2)/6.

Math has rules it has to follow in order to maintain consistency. If you break them, you get garbage. This is particularly true when dealing with infinite series.

[JusticeZero]

You need to have a non-uniform distribution, and you need to define it. We already have a practical dice-based method of doing this as well - exploding dice.
The two methods listed didn't have the advantages of the method I described of using percentile with exploding tails; that generates a result between 0 and 1, which is a good range to plug into formulas, but has infinitely expansible tails where you can track the low probability results.

[Chronos]

Quoth Sith_happens:

It is in fact less true, because the latter of those is an actual sum while the former is the result of a completely different operation that's merely sometimes referred to as a "sum" because it serves a similar purpose in the select problems to which it applies.
An "actual sum" has exactly two arguments, so by that line of reasoning, neither of those is an "actual sum". It is often convenient, however, to extend the definition of "sum" to include other concepts, such as the sum of an infinite sequence of numbers. Extend the definition in one way, and you get one of those examples; extend it in a different way, and you get the other. Both are equally valid.


Quoth Drachasor:

First, the sum of all natural numbers does not add up to -1/12. The "proofs" of this rely on a lot of blatantly wrong "math."
That's like saying that capturing en passant is a blatantly wrong chess move. The math is just as valid as math you're perfectly comfortable calling "right".

[Svata]

Either that, or mashed potatoes.

My favorite result, though, was the color flargbuon. Its the smell of a pear mixed with the texture of half-rotten buffalo hide.

[Irk]

My favorite result, though, was the color flargbuon. Its the smell of a pear mixed with the texture of half-rotten buffalo hide.

Flargbuon has actually 0 results on google.

[broodax]

The two methods listed didn't have the advantages of the method I described of using percentile with exploding tails; that generates a result between 0 and 1, which is a good range to plug into formulas, but has infinitely expansible tails where you can track the low probability results.

I'm not sure what to do with your results, as they are real numbers between 0 and 1, not natural numbers, and the set of possibilities is rather limited (e.g. you can't get a result of .889). Is there some step you're taking afterward to covert it to a whole number?

[ddude987]

That's like saying that capturing en passant is a blatantly wrong chess move. The math is just as valid as math you're perfectly comfortable calling "right".

I would disagree with your comparison. There are scenarios en passant is the correct move, regardless of mathematical proof, because while it is theoretically possible to emulate every chess game possible and "prove" en passant is never the right play, chess is also a mind-game and therefore mutable, whereas math is non-mutable.

[Chronos]

Math is also a mind-game and is mutable. And I don't mean arguing that en passant is sub-optimal; I mean arguing that it's against the rules. You could play a chess variant that doesn't allow en passant (which used to be the normal rules, once), and it's still an interesting game, just a slightly different game than standard modern chess. Likewise, you could play a math variant that doesn't allow summing all of the natural numbers, and it's still an interesting game, just a slightly different game than standard modern mathematics.

[georgie_leech]

Math is also a mind-game and is mutable. And I don't mean arguing that en passant is sub-optimal; I mean arguing that it's against the rules. You could play a chess variant that doesn't allow en passant (which used to be the normal rules, once), and it's still an interesting game, just a slightly different game than standard modern chess. Likewise, you could play a math variant that doesn't allow summing all of the natural numbers, and it's still an interesting game, just a slightly different game than standard modern mathematics.

The objection isn't that he couldn't do it because he broke the rules, but that he misrepresented what he did. He didn't sum the natural numbers, but some properties of the natural numbers. It's related, but he didn't actually sum all the natural numbers, because "addition" in the sense of what it normally means doesn't apply.

[Zweisteine]

How would one go about implementing a die roll where the result was anything from zero to infinite?

It's not quite big enough, but I would recommend the catenative doomsday dice cascader (http://www.mspaintadventures.com/extras/ps000020.html).

[eggynack]

The objection isn't that he couldn't do it because he broke the rules, but that he misrepresented what he did. He didn't sum the natural numbers, but some properties of the natural numbers. It's related, but he didn't actually sum all the natural numbers, because "addition" in the sense of what it normally means doesn't apply.
Indeed. It'd be like saying, "You can't capture like that," when someone uses en passant, but not explaining at any point, either before or during the game, that you're playing a variant of chess in which that's the case.

[Sith_Happens]

Flargbuon had actually 0 results on google.

FTFY. Now it has 1 result.:smallwink:

[Drachasor]

An "actual sum" has exactly two arguments, so by that line of reasoning, neither of those is an "actual sum". It is often convenient, however, to extend the definition of "sum" to include other concepts, such as the sum of an infinite sequence of numbers. Extend the definition in one way, and you get one of those examples; extend it in a different way, and you get the other. Both are equally valid.

Except they aren't.



That's like saying that capturing en passant is a blatantly wrong chess move. The math is just as valid as math you're perfectly comfortable calling "right".

Except it isn't. It hinges on blatantly wrong summations that if you tried in ANY mathematics course you wouldn't even get partial credit.

Math has rules, and that "summation" breaks them. It's wrong.

Chess has rules, and en passant doesn't break them. It's ok.

For instance, the sum of 1-1+1-1+1-1...doesn't converge on ANYTHING. So saying "well, it's just the average" is idiotic. Any first year math student should be able to tell you that.

For another, you can't get a negative number by adding two positive numbers, which should be the first indication you've really messed up somewhere.

I could go on. There are a lot of fundamental errors made in that "proof."

[Chronos]

If you did it in a mathematics course taught by an actual mathematician, then yes, they would accept it. Most people think otherwise, because the closest they've ever come to math is what they've had in high school and elementary school (most of which aren't even math courses at all).

[Alent]

If you did it in a mathematics course taught by an actual mathematician, then yes, they would accept it. Most people think otherwise, because the closest they've ever come to math is what they've had in high school and elementary school (most of which aren't even math courses at all).

Uh... was this supposed to be in blue text, an inappropriate real world reference, or is there some kind of mysterious thing about higher level math that separates it from math?

[georgie_leech]

If you did it in a mathematics course taught by an actual mathematician, then yes, they would accept it. Most people think otherwise, because the closest they've ever come to math is what they've had in high school and elementary school (most of which aren't even math courses at all).

Again, what he's doing though isn't summing the set of natural numbers, he's summing the values of properties related to the set of natural numbers. It's not a sum in the traditional sense; he's not adding every single natural number together to get his result.

[Drachasor]

If you did it in a mathematics course taught by an actual mathematician, then yes, they would accept it. Most people think otherwise, because the closest they've ever come to math is what they've had in high school and elementary school (most of which aren't even math courses at all).

No, they wouldn't. As a math major I have to thoroughly disagree.

The "proof" is full of BS. Its the same level of basic errors that get you 1=0.

[Chronos]

Uh... was this supposed to be in blue text, an inappropriate real world reference, or is there some kind of mysterious thing about higher level math that separates it from math?
No, I said exactly what I meant there. Most students won't take any math courses at all until at least high school geometry. Before then, you just have arithmetic and a really limited special case of algebra.

[Phelix-Mu]

No, I said exactly what I meant there. Most students won't take any math courses at all until at least high school geometry. Before then, you just have arithmetic and a really limited special case of algebra.

Math generally builds upon itself. Arithmetic (also math) is pretty much always useful, and the proofs often introduced in geometry are an important form of reasoning that endures into the highest levels of theoretical math.

You can't really disparage the small bits without tarnishing the whole construct.

[eggynack]

No, I said exactly what I meant there. Most students won't take any math courses at all until at least high school geometry. Before then, you just have arithmetic and a really limited special case of algebra.
Yeah, I've heard that real math only starts somewhere as high up as reasonably complicated calculus. A bit of that geometric proof stuff might qualify in some manner, though not to the greatest extent. It feels like I'm always finding out that what I've done before doesn't qualify as math for some reason or another, and it tends to be a pretty true thing. I think I'm doing some math currently though, at least, though it remains to be seen whether or not I'll be proven wrong in the future.

Edit:
Math generally builds upon itself. Arithmetic (also math) is pretty much always useful, and the proofs often introduced in geometry are an important form of reasoning that endures into the highest levels of theoretical math.

You can't really disparage the small bits without tarnishing the whole construct.
Arithmetic isn't unimportant, and it's not really a bad thing. It's just also not really math. I've never really been sure where the cutoff is, as I've noted above.

[Drachasor]

No, I said exactly what I meant there. Most students won't take any math courses at all until at least high school geometry. Before then, you just have arithmetic and a really limited special case of algebra.

Arithmetic is a kind of math.


Yeah, I've heard that real math only starts somewhere as high up as reasonably complicated calculus. A bit of that geometric proof stuff might qualify in some manner, though not to the greatest extent. It feels like I'm always finding out that what I've done before doesn't qualify as math for some reason or another, and it tends to be a pretty true thing. I think I'm doing some math currently though, at least, though it remains to be seen whether or not I'll be proven wrong in the future.

Edit:
Arithmetic isn't unimportant, and it's not really a bad thing. It's just also not really math. I've never really been sure where the cutoff is, as I've noted above.

People who tell you that are math snobs that ignore reality in order to belittle other people. Arithmetic is math.

[eggynack]

People who tell you that are math snobs that ignore reality in order to belittle other people. Arithmetic is math.
Seems probable enough.

[georgie_leech]

Arithmetic is a kind of math.



People who tell you that are math snobs that ignore reality in order to belittle other people. Arithmetic is math.

"That's not a knife." (https://www.youtube.com/watch?v=WWl8EbNN8NM)

[Chronos]

If you're doing proofs, it's math. If you're not, it's not. Arithmetic is, of course, important, but then, so is literature. If I told you that literature isn't math, or that arithmetic isn't literature, you wouldn't be offended by those statements. Why be offended by the statement that arithmetic isn't math?

[Phelix-Mu]

arithmetic

1.
the branch of mathematics dealing with the properties and manipulation of numbers.

Alright, so, I might have to agree with the math snobs comment. You either take math as a cohesive whole, or you just chuck the whole thing. One part isn't inherently better than the other, and, as evidenced by popular perception of the difficulty of math, inability to properly use the simple bits will greatly inhibit the use of the complex bits.

As a veteran of multivariable calculus and other high-level math courses, I can tell you that most of my errors in multi-page solutions dealt with simple math errors that came from having to do huge numbers of simple operations in the course of solving a problem. Human error and something easily remedied.

[Slipperychicken]

No, they wouldn't. As a math major I have to thoroughly disagree.

The "proof" is full of BS. Its the same level of basic errors that get you 1=0.

It should trip anyone's BS-detector, but to understand why it's wrong, it helps to know something about how averages work.

[Drachasor]

"That's not a knife." (https://www.youtube.com/watch?v=WWl8EbNN8NM)

Touche. It could be for other reasons such as part of an intimidate check.

[georgie_leech]

Touche. It could be for other reasons such as part of an intimidate check.

Heh, you misunderstand, I agree with you. It's clear that both are knives, but one is much larger and pointier; I've always viewed the "that's not math" idea as something similar.

[Drachasor]

Heh, you misunderstand, I agree with you. It's clear that both are knives, but one is much larger and pointier; I've always viewed the "that's not math" idea as something similar.

I was agreeing with you though! He's not saying that as a knife snob (I don't think), but just to scare the crap out of the thug. Granted though, it is unclear.

You might also say something like that because of a misunderstanding of what math is or a number of other reasons. But yeah, fundamentally it is wrong whatever the reason for saying it. A Scotsman fallacy.


It should trip anyone's BS-detector, but to understand why it's wrong, it helps to know something about how averages work.

And how infinite sums work. The "proof" has a lot of errors in it.