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Had an Idea, Thought i'd post it.

 

it would be nice to see X in avadon. He stepped into a portal to another dimension, thus it would fit, Also, X pwns tongue

 

Eh, Just an idea. Dismiss it if you may but i like it tongue

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Originally Posted By: CRISIS on INFINITE SLARTIES
frpwns


I was unaware that the Nine-Headed Cave Cow dished out pwnage. Although that was a hilarious tyop...


And no. If Jeff wanted crossover Avernum/Geneforge/that one game with the Scottish people in it/Avadon games, he'd make them. And it would be seen as the ravings of a madman, unless thee Ecksian Skull said it (To the best of my knowledge, that is the only other time there is a direct reference to the other series in-game)

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Gah i didnt say cross avernum and avadon.

 

I just suggested X be put in as well He had to go to Some random dimension. For all i care you can wipe his memory of the previous dimension -.-

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You could always write a fanfiction where that happens. I'm sure EVERYBODY would read it.

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Originally Posted By: Student of Trinity
Originally Posted By: Dantius
Originally Posted By: CRISIS on INFINITE SLARTIES
frpwns

... a hilarious tyop...

Oh ye of little faith.


According to the infinite number of universes theory there is at least one universe where these are correct spellings. smile

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Originally Posted By: Randomizer
Originally Posted By: Student of Trinity
Originally Posted By: Dantius
frpwns

... a hilarious tyop...

Oh ye of little faith.


According to the infinite number of universes theory there is at least one universe where these are correct spellings.



Perhaps,but then again maybe that particulate spelling exists not.

or in every other universe but this one.

Someone Quote This!!!!!

Oh noes My quote brooke for randomizer.. ~!!! ! ! ! !

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Originally Posted By: Randomizer

Originally Posted By: Student of Trinity
...

According to the infinite number of universes theory there is at least one universe where these are correct spellings.


The real numbers are uncountably infinite. That doesn't mean that threeve exists.

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Originally Posted By: Lt. Sullust
Originally Posted By: Randomizer

Originally Posted By: Student of Trinity
...

According to the infinite number of universes theory there is at least one universe where these are correct spellings.


The real numbers are uncountably infinite. That doesn't mean that threeve exists.
Nonsense. Since an infinite number to transcendental numbers exist, there must be a name for all of them. I simply need to define "threeve" as "the irrational number between 3 and pi given by the equation [insert equation here]".

Boom, instant threeve.

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Wow, more of classical X humor in new games would be really great, I would love to have more quests to destroy his summoned or created failed experiments smile

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I should've perhaps pointed out that my definition of threeve was a number that is equally distant from 3 and 5, but that is not 4.

 

The point being that an infinite set need not contain everything. But I think we're getting off topic.

 

...

 

I'm not sure including 'X' would be worthwhile; maybe it's time we move on from Exile/Avernum.

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Continuing to drag things offtopic, one of the cool things about numbers is that there aren't names for most of them. In fact, almost all numbers can't be specified in any way whatsoever.

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Well, "most" is a little bit slippery there. But I think it's reasonable to say that many numbers can't be specified. What's more, many difficult numbers aren't obviously problematic. Who would guess that most whole numbers, if they can be expressed, require so much work that it's not worth the effort to invent a way to express them?

 

—Alorael, who is pretty sure someone has had enough X for today.

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Well, we can use Douglas Adams logic here:

1. There is an infinite number of numbers, by definition.

2. We have only a finite number of names for them.

3. A noninfinte number divided by an infinite number is zero.

4. Therefore, no numbers exist, and any and all numbers you meet are a figments of your demented imagination.

 

Q.E.D.

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Originally Posted By: Dantius
3. A noninfinte number divided by an infinite number is zero.
4. Therefore, no numbers exist, and any and all numbers you meet are a figments of your demented imagination.


First, I fail to grasp your leap between these two steps.

Second, a non-infinite number divided by infinity is undefined. The limit of such an expression is zero, but an actual answer does not exist. I guess you could say that's similar to zero, at least for your argument.

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We don't have a finite number of names for them. There is at least one number-naming system which allows for recursive, and therefore potentially infinite, naming. A googolplexplexplexplexplexplexplexplex...

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Originally Posted By: Word Slaad
Well, "most" is a little bit slippery there.


Not really. What it means is that if you pick a real number at random from within any given range, the probability that it's one that can be specified is 0.

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Man, Infi, I hate Infi, but this is what they teach there:

 

There is a proof somewhere that there are more non-rational (fancy J if I'm getting the wording wrong) numbers than rational numbers (fancy Q) even though they are both infinite.

 

That said,

 

All rational numbers have a "name" (even the big ones can still be written as a very long number such as 1*10^100000000000+5*10^55+... and so can be read if given enough time :))

 

some non-rational numbers, such as pi or the squared root of any prime number, have "names" and so any multiplication of them with a rational number has a "name" (maybe even addition can be dragged in this way).

 

The question that now remains is which is bigger:

all non-"named" non-rational numbers or the unity of all rational numbers with all "named" non-rational numbers.

 

And lets leave complex numbers out of this, ok?, please?

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Originally Posted By: No_More_PLL_Ever

There is a proof somewhere that there are more non-rational (fancy J if I'm getting the wording wrong) numbers than rational numbers (fancy Q) even though they are both infinite.


It's a diagonalisation proof, I think. Basically, if you try to set up any kind of correspondence between rationals and irrationals, you'll find yourself ending up with an infinite number of irrational numbers for every rational number.

Quote:
The question that now remains is which is bigger:
all non-"named" non-rational numbers or the unity of all rational numbers with all "named" non-rational numbers.


If I recall correctly the irrationals have the same cardinality as the reals, so adding in the rational numbers doesn't make the set "bigger".

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Originally Posted By: Dantius
Nonsense. Since an infinite number to transcendental numbers exist, there must be a name for all of them.
As nice as it may seem to posit that everything has a unique name, it doesn't really work out like that in practice. There are numerous nameless numbers (probably all of which are irrational).

Originally Posted By: Lt. Sullust
The point being that an infinite set need not contain everything.
Quite true. In fact, I'd go even further and point out that an infinite set cannot contain everything (no set can contain everything).

Originally Posted By: Dantius
Well, we can use Douglas Adams logic here:
1. There is an infinite number of numbers, by definition.
2. We have only a finite number of names for them.
3. A noninfinte number divided by an infinite number is zero.
4. Therefore, no numbers exist, and any and all numbers you meet are a figments of your demented imagination.

Q.E.D.
Point four does not follow from the premise; in fact, it directly contradicts the premise. Thus it cannot be called a conclusion.

Also, what's the purpose dividing the number of named numbers by the total number of numbers? Seems useless to me. Now, dividing the total number of numbers by the number of named numbers could be useful; this gives an infinite number, of course.

Originally Posted By: CRISIS on INFINITE SLARTIES
We don't have a finite number of names for them. There is at least one number-naming system which allows for recursive, and therefore potentially infinite, naming. A googolplexplexplexplexplexplexplexplex...
Considering that there is a generative naming system for rational numbers that could be applied indefinitely, yes, there are an infinite number of numbers with names. Though your example isn't really one of them as far as I know.

And there are generative naming systems for irrational numbers as well, though this certainly doesn't cover the entire domain of irrational numbers. Plus there are a number of irrationals that have special names, such as e, phi, and pi.

Originally Posted By: Lilith
Originally Posted By: Word Slaad
Well, "most" is a little bit slippery there.


Not really. What it means is that if you pick a real number at random from within any given range, the probability that it's one that can be specified is 0.
Not really. There's a pretty good chance that you'll pick one that has a name.

Originally Posted By: No_More_PLL_Ever
All rational numbers have a "name" (even the big ones can still be written as a very long number such as 1*10^100000000000+5*10^55+... and so can be read if given enough time :))

some non-rational numbers, such as pi or the squared root of any prime number, have "names" and so any multiplication of them with a rational number has a "name" (maybe even addition can be dragged in this way).
Not just the square root of prime numbers; the square root of any non-square number, the cube root of any non-cube, the nth root of any non-nth-power... and that's not the only set of functions that generates irrationals from rationals in a systematic way. There's the log functions, the trigonometric functions... even regular operations such as addition, subtraction, multiplication, division, and exponentiation.

Originally Posted By: No_More_PLL_Ever
The question that now remains is which is bigger:
all non-"named" non-rational numbers or the unity of all rational numbers with all "named" non-rational numbers.
Well, that's a very good question. It sounds like it would be pretty difficult to answer, since there are so many different ways to name irrational numbers.

Originally Posted By: No_More_PLL_Ever
And lets leave complex numbers out of this, ok?, please?
Oddly, complex numbers don't complicate matters all that much. Their effect is equivalent to introducing a single additional named irrational number which can then have any operation applied to it to produce a myriad of other numbers. Except of course i is not irrational.

Originally Posted By: No_More_PLL_Ever

There is a proof somewhere that there are more non-rational (fancy J if I'm getting the wording wrong) numbers than rational numbers (fancy Q) even though they are both infinite.
I'm not entirely sure whether the proof actually proves that the number of irrational numbers exceeds the number of rationals (though I wouldn't be surprised if it does); all I remember is that it proves the number of real numbers to exceed the number of rationals.

Originally Posted By: Lilith
If I recall correctly the irrationals have the same cardinality as the reals, so adding in the rational numbers doesn't make the set "bigger".
If this is the case, then yes, I'm pretty sure you're right that it doesn't make the set bigger.

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Originally Posted By: Celtic Minstrel

Not really. There's a pretty good chance that you'll pick one that has a name.


My understanding was that the set of transcendental numbers is of the same cardinality as the reals while the set of algebraic numbers (which are the numbers that can be named systematically, more or less) is the same cardinality as the natural numbers, and almost all of the transcendentals don't have names, so mathematically the probability you'll get a number with a name is 0.

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No, the probability can't be zero, simply because there are numbers with a name in your chosen range. The probability might be infinitesimal, but not zero.

 

As for cardinalities, apparently the transcendentals are uncountably infinite (same cardinality as reals) and the algebraics are countably infinite (same cardinality as naturals), so on that count you would be correct.

 

The number of transcendentals with names would be countably infinite; for each transcendental with a simple name (e, pi, ln(3), etc), you can derive an infinite number of additional named transcendentals.

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Originally Posted By: Celtic Minstrel
No, the probability can't be zero, simply because there are numbers with a name in your chosen range. The probability might be infinitesimal, but not zero.


Infinitesimal numbers don't exist in standard constructions of mathematics. Dividing a finite number by a countably infinite number, or a countably infinite number by an uncountably infinite number, yields 0. For example, the probability of selecting a random real number from the interval (1,3) and getting 2 is equal to zero, even though 2 is included in that interval.

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Originally Posted By: CRISIS on INFINITE SLARTIES
A googolplexplexplexplexplexplexplexplex...
...plexplex...plex *BOOM*

That explosion nearly cracked the record...the record...the record...the record...the record... tongue

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This is a contradiction; since 2 is included in that interval, it is possible to get a 2 when randomly selecting a number from that interval; however, a probability of 0 means that the event is impossible.

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Originally Posted By: Celtic Minstrel
This is a contradiction; since 2 is included in that interval, it is possible to get a 2 when randomly selecting a number from that interval; however, a probability of 0 means that the event is impossible.


In the strict mathematical sense of probability, that's not what a probability of 0 means. Quoth Wikipedia:

Quote:
An impossible event has a probability of 0, and a certain event has a probability of 1. However, the converses are not always true: probability 0 events are not always impossible, nor probability 1 events certain.


What a probability of 0 actually means is that in an arbitrarily large number of trials you will still expect to see the event in question 0 times.

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Yeah, that makes sense. An infinitesimal number would be something along the lines of point zero repeating one, right? As much as I dislike it conceptually, you can use algebra to prove that the above number equals zero.

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Originally Posted By: Lilith
Originally Posted By: Word Slaad
Well, "most" is a little bit slippery there.


Not really. What it means is that if you pick a real number at random from within any given range, the probability that it's one that can be specified is 0.

I maintain that when you start examining the cardinality of the set of rational numbers and the set of transcendental numbers you're working with a funny sort of "most," as the debate over zero probability attests.

—Alorael, who points to what happens over the interval (2-e,2+e), where e is infinitely small. Answer: depending on how infinitely small it is, the probability of selecting 2 is either 0 or 1. There is never a pretty good but not quite certain chance you'll get 2.

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Originally Posted By: Celtic Minstrel

Originally Posted By: No_More_PLL_Ever
some non-rational numbers, such as pi or the squared root of any prime number, have "names" and so any multiplication of them with a rational number has a "name" (maybe even addition can be dragged in this way).
Not just the square root of prime numbers; the square root of any non-square number, the cube root of any non-cube, the nth root of any non-nth-power... and that's not the only set of functions that generates irrationals from rationals in a systematic way. There's the log functions, the trigonometric functions... even regular operations such as addition, subtraction, multiplication, division, and exponentiation.

You're slightly misinterpreting, I imagine: he's not saying that "only the square roots of primes are irrational"; he's saying that "the square roots of primes can be said to have 'names' and then you can start generating the names of other irrationals from there."

Nonetheless, you'd need the nth roots of all primes, plus a bunch more, and you'd still never accomplish the task because there are uncomputable numbers and as long as a number can't be computed, you can't meaningfully give it a name (since you can't call it 'log of pete' or 'cosine of mike' or much of anything else, as it can't be given as a function evaluated on some argument that can be computed by a finite, terminating algorithm.)

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Another way of justifying "most":

If you let I(x) = { 1 if x can be named ; 0 if not}, then the integral of I(x) over any range is zero (assuming you're using a method of integration that's powerful enough to integrate a function that crazy).

 

Edit: Well, I say "another" but really I mean "the same but presented differently"

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Numbers don't 'exist' - people made them up. When dealing with what is it's good to bear that it mind. Mathematics only deals with what works (computes or whatever).

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Originally Posted By: waterplant
Numbers don't 'exist' - people made them up. When dealing with what is it's good to bear that it mind. Mathematics only deals with what works (computes or whatever).


You must not have studied alot of mathematics then smile

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Though one could argue that numbers don't exist (and in the most abstract sense, they might be right), numbers do arise naturally from simple observations of reality.

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Originally Posted By: Celtic Minstrel
numbers do arise naturally from simple observations of reality.
Where? I've never seen one before.

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What Monroe said. Or more precisely, what the heck does "arise naturally" mean? Do you mean "are typically arrived at by the human mind due to their being the simplest and most efficient tool for dealing with abstract quantities"?

 

That's a reasonable statement (albeit not immune from debate) that points to some of the relevant qualities of numbers as a class. But let's not pretend we're talking about spontaneous generation here. This is a clear case of intelligent design!

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Originally Posted By: Monroe
Originally Posted By: Celtic Minstrel
numbers do arise naturally from simple observations of reality.
Where? I've never seen one before.
You've never seen a number directly, of course, because they're an abstract concept; but the concept of number comes out of quantity and counting. Indirectly, numbers exist everywhere; you have ten fingers; you have two eyes. Perhaps you ate six apples. Or there are twelve distinct clouds in the sky. Maybe you haven't eaten for four days. So, numbers may not manifest themselves physically in reality, but they arise naturally from reality simply by counting.

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Those six apples were, in reality, each a unique entity, or sets of many entities, or a single set as a group. The six (or any other number that one might apply) only exists in our minds as we need apply it.

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