Probability, for all you logicians

[Roman Candle]

I came up with this thought experiment the other day, and I seemed to come to some odd conclusions. If you've done a course in philosophy, specifically logic, not that particular brand of moral and/or paranoid bullshit which people like to call philosophy, then this might make sense to you.

You have two mechanisms which, based on some kind of totally random event, atomic decay or some kind of quamtum event or summat, continusly generate random numbers. Any rational real number can be found. As there are an infinite number of such values which could be found, and they are all equally likely to be found, it seems that the chance of both computers coming up with the same number is infinitely unlikely. In fact, the probability of each value is 1/(1/0), making each one infinitely unlikely. In that case, it seems infinitely unlikely that a number will be chosen at all. However, it is still entirely possible that both computers will choose a number, and entirely possible that they will both choose the same number. Now, I'm sure I've gone wrong somewhere here. Any comments?

Edit:
Does this prove that it's impossible to generate a number randomly from an infinite range?

 

[Chaosg1]

Computers don't generate numbers... They have a list of numbers that they choose from one that means that the computer would crash when trying to get a number of a Infinite number.

EDit:Bah Too tired to think...

 

[macchia]

"Does this prove that it's impossible to generate a number randomly from an infinite range?"

Without a cap, yes. However one must assume by the smallest measure over the largest range a 'maximum' number exists. That is, a number large enough to encompass any measure. This is assuming the universe isnt infinite, which many no longer believe it is. In which case, nothing is infinite and this is possible.

 

[Roman Candle]

Chaosg1, I carefully didn't use the word computer, because computers can't generate real random numbers.
macchia, I see what you mean, but even if you had a number that could express the highest value in the universe in it's most fundemental unit, it wouldn't be the highest number possible. For instance, you could find that number and double it, for fun.

Anyway, thanks for your comments.

 

[lunarhiro2002]

No it doesn't prove that you cannot generate a number randomly from an infinite list of numbers. All it proves is that the way you layed out is the wrong way to do it...

 

[tensuke]

I just picked up The Infinite Book a few weeks ago, it's a really good read on the subject of infinty. It explores the history and plenty of theories concerning it.
However, I'm no good with probability so I'll stay outta this one. :P

 

[macchia]

Chaosg1, I carefully didn't use the word computer, because computers can't generate real random numbers.
macchia, I see what you mean, but even if you had a number that could express the highest value in the universe in it's most fundemental unit, it wouldn't be the highest number possible. For instance, you could find that number and double it, for fun.

Anyway, thanks for your comments.

Well I suppose, but then using our number system we can go below absolute zero as well, it doesnt mean the universe can. I suppose my point is the number you'd express doubling the maximum value would be as logically relevent as a dragon. We can create it, sure with our number system, its just it wouldnt be applicable to anything. Idunno, there's no good answer to your question.

 

[DaGuyWitBluGlasses]

"The infinitessimal"

Remember, the first one is a given, so it does not need to be calculated. it is one.

So the odds are 1/infinity

E.g. if you roll 2 six sided dice, the odds of getting double is 1/6. Because whatever the first one rolls, the second one can, so the first one doesn't count in the odds.

 

[FzGhouL]

You can't calculate what the probably of any number in a continuous random variable, you may only calculate a closed range of numbers.

Note that 1.1<=x<=2.2 is equivalent to 1.1 < x <2.2 because of that fact.

With infinite degrees of accuracy, your probability is so infinitesimal that it is considered 0, as it is an undefinable number 1/infinity.

There is no such thing as a maximum number.

 

[macchia]

There's probably some poetry on life found in that fact, that zero has nothing to accompany it on the opposite end.</lame offtopic respit>

 

[FzGhouL]

Macchia, all numbers are opposite of zero.

 

[macchia]

Not really. The opposite of me having 1 apple and you having nothing is you having 1 apple and me having nothing. So the oppsite of any given number is its negative. Zero has no opposite unless you include theoreticals like infinity or everything.

 

[Roman Candle]

No, the opposite of you having an apple and FZ not having an apple is FZ not having an apple and you having an object which would perfectly obliterate any apple which came to occupy the same space without a trace. No, wait, since an apple exists, the opposite of an apple is something which if it came into contact with an apple would be perfectly erased, and which does not exist.

Don't confuse quantity with number :p Anyway, if you want to think of 10 as the opposite of -10 or (-1)(10), then the opposite of 0 = (-1)(0) = 0.

 

[macchia]

*stares blankly*
Confession. Im out of my depth.
*tiptoes out of thread*

 

[Krank The Tank]

No, the opposite of you having an apple and FZ not having an apple is FZ not having an apple and you having an object which would perfectly obliterate any apple which came to occupy the same space without a trace. No, wait, since an apple exists, the opposite of an apple is something which if it came into contact with an apple would be perfectly erased, and which does not exist.

Don't confuse quantity with number :p Anyway, if you want to think of 10 as the opposite of -10 or (-1)(10), then the opposite of 0 = (-1)(0) = 0.

I think I see what you're saying here. The opposite of 1 apple is -1 apple. But you can't have -1 of an apple, because if you did there would be some sort of void where there should be no apples. And that void would be -1 of anything, so pretty much anything that attempts to be in the same spot as that void would be obliterated. Is that what you mean?

This is pretty much unfathomable, actually, since what -1 of an apple is, is essentially like a singularity, which is something that exists, therefore you have to be holding something that does not exist, which is impossible because to hold something it must exist.

To get back to the original question, "Does this prove that it's impossible to generate a number randomly from an infinite range?" As long as you don't use a computer, it is, for reasons stated earlier in the thread. But what you are talking about is so improbable that if the world were based on the probability of this idea, we would be living in the Matrix. And since there are an infinite amount of numbers, it is infinitely improbable that these two things would pick the same number...which is exactly what you guys were saying earlier *slaps head*

 

[DaGuyWitBluGlasses]

"Antonyms" are words that have opposing definitions.

"Opposites" can always be made to have the same (general) definition, though they themselves are not interchangeable
e.g. A left hand is made up of 4 fingers, one thumb, a palm... a right hand is made up of 4 fingers, one thumb, a palm, but there's no way you can twist or turn your right hand into th epattern that makes your left hand.

So 1 is the opposite of -1 as they can be both made to have the same meaning (1 away from zero). Zero is not the opposite of 1, since they cannot be given the same definition.

There's is no opposite of 1 apple (unless some symbolism is attached).

(psst ... It's not possible to generate a number from an infinite range, as everything in the universe is finite)

 

[FoxDemonSoavi]

I have -1 apple. I owe someone an apple. The opposite of having one apple is oweing someone an apple. Does that work?

 

[DaGuyWitBluGlasses]

I have -1 apple. I owe someone an apple. The opposite of having one apple is oweing someone an apple. Does that work?

Nope, because having something, and owing someone can't have the same definition.

The opposite of you owing someone an apple is when someone owes you an apple.

 

[FzGhouL]

deleted

 

[DaGuyWitBluGlasses]

Opposite of having is not having.
Having 0 is not having.

Tah-dah.

Opposites must be mutual.

Since there is no way you can deduce 1 as the opposite of zero, then 0 cannot be the opposite of 1.