Forum Index Register Members List Events Mark Forums Read Help

 International Skeptics Forum Infinite Sets and Probability

 Welcome to the International Skeptics Forum, where we discuss skepticism, critical thinking, the paranormal and science in a friendly but lively way. You are currently viewing the forum as a guest, which means you are missing out on discussing matters that are of interest to you. Please consider registering so you can gain full use of the forum features and interact with other Members. Registration is simple, fast and free! Click here to register today.
 29th July 2018, 11:34 PM #1 Fudbucker Philosopher   Join Date: Jul 2012 Posts: 8,254 Infinite Sets and Probability Suppose I awake in an unknown hotel room. The only clue as to my whereabouts is the fact that I know I'm in one of two sets of infinite hotel rooms: the Ritz set or the Motel 6 set. In the Motel 6 set, for every opulent room, there are a billion dingy ones. In the Ritz set, it's the opposite. The room I wake up in is opulent. Does this allow me to conclude I'm probably in the Ritz set, or does the fact there are just as many dingy rooms as opulent rooms (since there are an infinite amount of both types of rooms in both sets) make a probability calculus impossible? Last edited by Fudbucker; 29th July 2018 at 11:56 PM.
 30th July 2018, 12:21 AM #2 MetalPig Illuminator     Join Date: Jan 2006 Location: 22, Acacia Avenue Posts: 3,021 I think this proves at you are immortal. __________________ Just drive.
 30th July 2018, 12:45 AM #3 MetalPig Illuminator     Join Date: Jan 2006 Location: 22, Acacia Avenue Posts: 3,021 Seriously though, I'm pretty sure we can conclude you are probably in the Ritz. Because although there are an infinite number of both types of room, their ratio is still a billion to one. __________________ Just drive.
 30th July 2018, 01:20 AM #4 Dave Rogers Bandaged ice that stampedes inexpensively through a scribbled morning waving necessary ankles     Join Date: Jan 2007 Location: Cair Paravel, according to XKCD Posts: 27,150 This is a pretty simple case of Bayes' Theorem. I haven't bothered to do the maths but it's pretty clear that, provided that you're a priori equally likely to have ended up in either hotel, then there's about a billion to one probability you're in the Ritz. If, on the other hand, you went out last night with ten billion drinking buddies, at some point in the evening youphoned the Ritz and they said they'd reserve one room for the first one of you to get there and all the others would have to go to the Motel 6, and you then all got blind drunk and you can't remember anything more than a vague memory of going to a hotel afterwards, then I'd say there's about a ten-to-one chance you're in the Motel 6. Dave __________________ Me: So what you're saying is that, if the load carrying ability of the lower structure is reduced to the point where it can no longer support the load above it, it will collapse without a jolt, right? Tony Szamboti: That is right
 30th July 2018, 01:34 AM #5 Robin Philosopher   Join Date: Apr 2004 Posts: 8,940 The probability that you are in the Ritz is either 1 or 0, you just don't know which. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 30th July 2018, 05:45 AM #6 ddt Mafia Penguin     Join Date: Dec 2007 Location: Netherlands Posts: 19,576 In neither. It's well-known the only hotel in the world with an infinite amount of rooms is Hilbert's Hotel. ETA: and what MetalPig and Dave Rogers said.. __________________ "I think it is very beautiful for the poor to accept their lot, to share it with the passion of Christ. I think the world is being much helped by the suffering of the poor people." - "Saint" Teresa, the lying thieving Albanian dwarf "I think accuracy is important" - Vixen Last edited by ddt; 30th July 2018 at 05:47 AM.
 30th July 2018, 06:37 AM #7 Robin Philosopher   Join Date: Apr 2004 Posts: 8,940 Well no, if you are sitting in a hotel room and it happens to be a room at Motel 6 then the probability that you are in the Ritz is 0. But if you are sitting in a hotel room and it happens to be a room at the Ritz, then the probability that you are in the Ritz is 1. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 30th July 2018, 06:44 AM #8 theprestige Penultimate Amazing   Join Date: Aug 2007 Posts: 28,407 I guess my question is the same as Fud's: Does the infinite set affect the probability calculation at all?
 30th July 2018, 06:56 AM #9 Dave Rogers Bandaged ice that stampedes inexpensively through a scribbled morning waving necessary ankles     Join Date: Jan 2007 Location: Cair Paravel, according to XKCD Posts: 27,150 Originally Posted by Robin Well no, if you are sitting in a hotel room and it happens to be a room at Motel 6 then the probability that you are in the Ritz is 0. But if you are sitting in a hotel room and it happens to be a room at the Ritz, then the probability that you are in the Ritz is 1. Since in either of these instances the outcome is completely known, probability theory is therefore inapplicable. Probability theory is applicable when we have incomplete information; for example, if you're sat in a hotel room but you don't know which hotel you're in. What's actually being discussed in this example is the relative probabilities of two future events, one and only one of which will occur when you find out which hotel you're in; one is that you find out you're in the Ritz, and the other is that you find out you're in Motel 6. Dave __________________ Me: So what you're saying is that, if the load carrying ability of the lower structure is reduced to the point where it can no longer support the load above it, it will collapse without a jolt, right? Tony Szamboti: That is right
 30th July 2018, 06:58 AM #10 Dave Rogers Bandaged ice that stampedes inexpensively through a scribbled morning waving necessary ankles     Join Date: Jan 2007 Location: Cair Paravel, according to XKCD Posts: 27,150 Originally Posted by theprestige I guess my question is the same as Fud's: Does the infinite set affect the probability calculation at all? Suppose you're about to look out of the window, and you know that it'll be dark roughly half of the time and light roughly the other half. Does the fact that there's an infinite number of possible instants that you could look out of the window affect the calculation that the probability of it being light is about 0.5? Any probability calculation over a continuous interval is in effect using an infinite set. Dave __________________ Me: So what you're saying is that, if the load carrying ability of the lower structure is reduced to the point where it can no longer support the load above it, it will collapse without a jolt, right? Tony Szamboti: That is right
 30th July 2018, 07:00 AM #11 Robin Philosopher   Join Date: Apr 2004 Posts: 8,940 Originally Posted by Dave Rogers Since in either of these instances the outcome is completely known, probability theory is therefore inapplicable. Probability theory is applicable when we have incomplete information; for example, if you're sat in a hotel room but you don't know which hotel you're in. What's actually being discussed in this example is the relative probabilities of two future events, one and only one of which will occur when you find out which hotel you're in; one is that you find out you're in the Ritz, and the other is that you find out you're in Motel 6. Dave It doesn't matter if it is known or not. The probability of being somewhere else than you are is 0, even if you don't know where you are. And the OP states: "Suppose I awake in an unknown hotel room" so it is not talking about two future events it is talking about present location. So if you awake in an unknown hotel room and it happens to be in Motel 6 then the probability that you are in the Ritz is 0. If you awake in an unknown hotel room and it happens to be in the Ritz, then the probability that you are in the Ritz is 1. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 30th July 2018, 07:13 AM #12 Robin Philosopher   Join Date: Apr 2004 Posts: 8,940 I mean assuming the room is not going to randomly change hotels between you waking up and finding out the name of the hotel you are in. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 30th July 2018, 07:25 AM #13 phunk Illuminator     Join Date: Aug 2007 Posts: 3,738 Originally Posted by Robin It doesn't matter if it is known or not. The probability of being somewhere else than you are is 0, even if you don't know where you are. And the OP states: "Suppose I awake in an unknown hotel room" so it is not talking about two future events it is talking about present location. So if you awake in an unknown hotel room and it happens to be in Motel 6 then the probability that you are in the Ritz is 0. If you awake in an unknown hotel room and it happens to be in the Ritz, then the probability that you are in the Ritz is 1. The answer may be predetermined, but it is unknown, and the probabilities still exist. There is a billion to one chance that you'll *learn* you're in one hotel vs the other.
 30th July 2018, 07:34 AM #14 jrhowell Critical Thinker   Join Date: Jun 2009 Posts: 482 I don't know if I am right mathematically, but if all I had to go on is that one piece of information (opulent room) and I had to stake my life on one choice or the other then I would pick the Ritz.
 30th July 2018, 07:36 AM #15 Robin Philosopher   Join Date: Apr 2004 Posts: 8,940 If the unknown room you happen to wake up in is in Motel 6 then there is a 0 probability that you will learn that you are in the Ritz (if you learn which hotel you are in at all). If the unknown room you happen to wake up in is in the Ritz then there is a probability of 1 that you will learn that you are in the Ritz (again, if you learn which hotel you are in at all). __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 30th July 2018, 07:36 AM #16 Dave Rogers Bandaged ice that stampedes inexpensively through a scribbled morning waving necessary ankles     Join Date: Jan 2007 Location: Cair Paravel, according to XKCD Posts: 27,150 Originally Posted by Robin It doesn't matter if it is known or not. The probability of being somewhere else than you are is 0, even if you don't know where you are. Suppose someone you know to be honest flips a fair coin and covers it with their hand, then says they'll agree to pay you \$2000 if it's heads provided you agree to pay them \$1 if it's tails. Do you reason that the odds are overwhelmingly in your favour and take the bet, or do you say that the probability of it being one of the two is already 1 and of the other is already 0 you can't tell which it is, so you don't know what to do? Dave __________________ Me: So what you're saying is that, if the load carrying ability of the lower structure is reduced to the point where it can no longer support the load above it, it will collapse without a jolt, right? Tony Szamboti: That is right
 30th July 2018, 07:38 AM #17 Robin Philosopher   Join Date: Apr 2004 Posts: 8,940 By the way, how are you doing your calculations? There are the same number of dingy rooms in both hotels. There are the same number of opulent rooms in both hotels. There is the same ratio of opulent to dingy rooms in both hotels. So why aren't you getting 50/50 Ritz or Motel 6? __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 30th July 2018, 07:38 AM #18 SOdhner Graduate Poster   Join Date: Apr 2010 Location: Arizona Posts: 1,724 Originally Posted by Dave Rogers Suppose you're about to look out of the window, and you know that it'll be dark roughly half of the time and light roughly the other half. Since that one is already 50/50 and his question is about whether or not an having countably infinite instances of two options causes everything to become 50/50 it probably won't help him. Originally Posted by Robin It doesn't matter if it is known or not. The probability of being somewhere else than you are is 0, even if you don't know where you are. Congratulations on being technically correct and also not making any attempt to be constructive in any way. Originally Posted by theprestige I guess my question is the same as Fud's: Does the infinite set affect the probability calculation at all? I think the main problem is it makes it really hard to word it in a valid way. Maybe impossible. We can't really talk about picking a room at random because we can't calculate probability with infinity. Narrowing it down to two hotels might in theory make it possible, but I'm not really certain. Probability and infinity don't play well together.
 30th July 2018, 07:39 AM #19 Worm Master Poster     Join Date: Jun 2006 Posts: 2,156 Some fundamental misunderstanding of probability theory going on here I think. __________________ "Violence is the last refuge of the incompetent" Isaac Asimov Not all cults are bad - I've joined a cult of niceness
 30th July 2018, 07:41 AM #20 Robin Philosopher   Join Date: Apr 2004 Posts: 8,940 Originally Posted by Dave Rogers Suppose someone you know to be honest flips a fair coin and covers it with their hand, then says they'll agree to pay you \$2000 if it's heads provided you agree to pay them \$1 if it's tails. Do you reason that the odds are overwhelmingly in your favour and take the bet, or do you say that the probability of it being one of the two is already 1 and of the other is already 0 you can't tell which it is, so you don't know what to do? Dave What does this have to do with the original question? __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 30th July 2018, 07:42 AM #21 Dave Rogers Bandaged ice that stampedes inexpensively through a scribbled morning waving necessary ankles     Join Date: Jan 2007 Location: Cair Paravel, according to XKCD Posts: 27,150 Originally Posted by Robin There are the same number of dingy rooms in both hotels. There are the same number of opulent rooms in both hotels. There is the same ratio of opulent to dingy rooms in both hotels. So why aren't you getting 50/50 Ritz or Motel 6? Because you've stated the problem incorrectly. The OP clearly states that the ratio of dingy to opulent rooms is the opposite in the two hotels - one billion to one in the Motel 6, one to one billion in the Ritz. Dave __________________ Me: So what you're saying is that, if the load carrying ability of the lower structure is reduced to the point where it can no longer support the load above it, it will collapse without a jolt, right? Tony Szamboti: That is right
 30th July 2018, 07:48 AM #22 Dave Rogers Bandaged ice that stampedes inexpensively through a scribbled morning waving necessary ankles     Join Date: Jan 2007 Location: Cair Paravel, according to XKCD Posts: 27,150 Originally Posted by Robin What does this have to do with the original question? It has to do with your rejection of a posteriori probability. If you don't want to discuss that, then please feel free to ignore it, but it might then be polite if you stopped replying to a question about a well-known aspect of probability theory by saying you don't believe in the underlying theory. Technically, it's off-topic to the thread. Dave __________________ Me: So what you're saying is that, if the load carrying ability of the lower structure is reduced to the point where it can no longer support the load above it, it will collapse without a jolt, right? Tony Szamboti: That is right
 30th July 2018, 07:49 AM #23 Dave Rogers Bandaged ice that stampedes inexpensively through a scribbled morning waving necessary ankles     Join Date: Jan 2007 Location: Cair Paravel, according to XKCD Posts: 27,150 Originally Posted by SOdhner I think the main problem is it makes it really hard to word it in a valid way. Maybe impossible. We can't really talk about picking a room at random because we can't calculate probability with infinity. Yes, we can. There is an infinite number of positive integers. What is the probability that a randomly chosen positive integer will be divisible by ten? Dave __________________ Me: So what you're saying is that, if the load carrying ability of the lower structure is reduced to the point where it can no longer support the load above it, it will collapse without a jolt, right? Tony Szamboti: That is right
 30th July 2018, 07:50 AM #24 Robin Philosopher   Join Date: Apr 2004 Posts: 8,940 Originally Posted by SOdhner Congratulations on being technically correct and also not making any attempt to be constructive in any way. It really depends on what point was supposed to emerge from this. As I said there are the same number of dingy rooms in both hotels, same number of opulent rooms in both hotels, same ratio of dingy to opulent rooms in both hotels - so I am interested in how is the calculation is being done. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 30th July 2018, 07:53 AM #25 Trebuchet Penultimate Amazing     Join Date: Nov 2003 Location: The Great Northwet Posts: 17,796 You're in the Ritz, having vastly over-estimated the number of oppulent rooms in Motel 6. __________________ Cum catapultae proscribeantur tum soli proscripti catapultas habeant.
 30th July 2018, 07:57 AM #26 Robin Philosopher   Join Date: Apr 2004 Posts: 8,940 Originally Posted by Dave Rogers Yes, we can. There is an infinite number of positive integers. What is the probability that a randomly chosen positive integer will be divisible by ten? Dave Well there are the same number divisible by ten as there are not divisible by ten, so I guess 0.5. Again, how is the calculation being made? __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 30th July 2018, 07:57 AM #27 ddt Mafia Penguin     Join Date: Dec 2007 Location: Netherlands Posts: 19,576 Originally Posted by Robin By the way, how are you doing your calculations? There are the same number of dingy rooms in both hotels. There are the same number of opulent rooms in both hotels. Yes, to be precise: those numbers are Aleph-naught. Originally Posted by Robin There is the same ratio of opulent to dingy rooms in both hotels. No, they're reverse. Originally Posted by Robin So why aren't you getting 50/50 Ritz or Motel 6? Because calculations with infinites don't work the same way as with finite numbers. Maybe this helps. Both the Ritz and Motel-6 have their rooms numbered 1, 2, 3, etc., ad infinitum, using all the natural numbers. In the Ritz, all rooms of which the number ends with 9 zeros are dingy, the other rooms opulent. In Motel-6, all rooms of which the number ends with 9 zeros are opulent, the rest dingy. (*) The room numbers are only displayed on the outside; there's nothing inside the room that tells you its number. (1) As soon as you wake up, someone phones you and tells your room number is lower/equal to 10^12. What is the probability now that you are in the Ritz? (2) As soon as you wake up, someone phones you and tells your room number is lower/equal to 10^15. What is the probability now that you are in the Ritz? (3) Repeat, with 10^18. (4) Repeat, with 10^21. Et cetera. (*) In the interest of giving a simple description, I've slightly changed the ratios from 1 billion to 1 to 999,999,999 to 1, but that shouldn't distract from the point. __________________ "I think it is very beautiful for the poor to accept their lot, to share it with the passion of Christ. I think the world is being much helped by the suffering of the poor people." - "Saint" Teresa, the lying thieving Albanian dwarf "I think accuracy is important" - Vixen
 30th July 2018, 07:58 AM #28 phunk Illuminator     Join Date: Aug 2007 Posts: 3,738 Originally Posted by Robin It really depends on what point was supposed to emerge from this. As I said there are the same number of dingy rooms in both hotels, same number of opulent rooms in both hotels, same ratio of dingy to opulent rooms in both hotels - so I am interested in how is the calculation is being done. No, there aren't the same number. Infinity is not a number. The sets being infinite doesn't matter. We're given the information that there is a fixed ratio of good to bad rooms in both hotels. It is therefore a simple probability of being in one type of room or the other, and given a random room of either type there is a simple probability of being in one hotel or the other.
 30th July 2018, 07:59 AM #29 Robin Philosopher   Join Date: Apr 2004 Posts: 8,940 Originally Posted by Dave Rogers Because you've stated the problem incorrectly. The OP clearly states that the ratio of dingy to opulent rooms is the opposite in the two hotels - one billion to one in the Motel 6, one to one billion in the Ritz. Dave No, there are infinitely many rooms. Motel 6 has infinitely many dingy rooms and infinitely many opulent rooms. The Ritz has infinitely many dingy rooms and infinitely many opulent rooms. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 30th July 2018, 08:00 AM #30 jrhowell Critical Thinker   Join Date: Jun 2009 Posts: 482 Originally Posted by Dave Rogers Yes, we can. There is an infinite number of positive integers. What is the probability that a randomly chosen positive integer will be divisible by ten? That raises a question in my mind. Can we truly choose randomly from an infinite set? Any positive integer we could actually pick would have to be from the lower part of that ordered set. In other words, no matter which number we pick there would always be more numbers in the set higher that the selected number than there are ones lower than the selected number. Seems biased to me. Maybe? Last edited by jrhowell; 30th July 2018 at 08:09 AM.
 30th July 2018, 08:02 AM #31 phunk Illuminator     Join Date: Aug 2007 Posts: 3,738 Robin, by your logic, picking a random number out of all possible integers has a 50/50 chance of it being divisible by 9342193475892734. Because there are an infinite number of integers divisible by that number, and an infinite number not divisible... Does that seem right to you?
 30th July 2018, 08:03 AM #32 Robin Philosopher   Join Date: Apr 2004 Posts: 8,940 Originally Posted by phunk No, there aren't the same number. Infinity is not a number. Put it this way then. There are as many opulent rooms in Motel 6 as there are dingy rooms. There are as many opulent rooms in the Ritz as there are dingy rooms. Quote: The sets being infinite doesn't matter. We're given the information that there is a fixed ratio of good to bad rooms in both hotels. It is therefore a simple probability of being in one type of room or the other, and given a random room of either type there is a simple probability of being in one hotel or the other. Are you saying there are more dingy rooms than opulent rooms in Motel 6? Or that there are more opulent rooms then dingy rooms in the Ritz __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 30th July 2018, 08:03 AM #33 SOdhner Graduate Poster   Join Date: Apr 2010 Location: Arizona Posts: 1,724 Originally Posted by Dave Rogers Yes, we can. There is an infinite number of positive integers. What is the probability that a randomly chosen positive integer will be divisible by ten? Well sure, but... um. Hang on I got my foggily-remembered stuff mixed up. I was thinking about calculating probability of picking a specific number or item rather than a category (divisible by ten), which... is that still... Anyway regardless of exactly how wrong I am (anywhere from 50% to 100%) I really like your example. So, to map it on to the example in the OP: There are infinite rooms in two hotels in town (and also the Hilbert but it's full and while they insist they can accommodate more we don't want to inconvenience an infinite amount of guests). Every billionth room at the Ritz is shabby, and every billionth room at the Sunshine Suites is fancy. Since they have room numbers it's easy to talk about them using just numbers, so just like you can ask about the odds of something being divisible by ten we can ask if it's divisible by a billion. So the odds of a randomly chosen room being an outlier at each hotel WOULD still be different, so it WOULD be something to base your guess off of. Cool. Last edited by SOdhner; 30th July 2018 at 08:06 AM.
 30th July 2018, 08:05 AM #34 Dave Rogers Bandaged ice that stampedes inexpensively through a scribbled morning waving necessary ankles     Join Date: Jan 2007 Location: Cair Paravel, according to XKCD Posts: 27,150 Originally Posted by Robin Well there are the same number divisible by ten as there are not divisible by ten, so I guess 0.5. Again, how is the calculation being made? Seriously, do you think the probability of picking a random integer divisible by ten is equal to the probability of picking one not divisible by ten, and do you think there's more than one way of calculating those probabilities? Dave __________________ Me: So what you're saying is that, if the load carrying ability of the lower structure is reduced to the point where it can no longer support the load above it, it will collapse without a jolt, right? Tony Szamboti: That is right
 30th July 2018, 08:06 AM #35 Robin Philosopher   Join Date: Apr 2004 Posts: 8,940 Originally Posted by phunk Robin, by your logic, picking a random number out of all possible integers has a 50/50 chance of it being divisible by 9342193475892734. Because there are an infinite number of integers divisible by that number, and an infinite number not divisible... Does that seem right to you? I am not sure how you are even proposing to select numbers randomly from an infinite set. If you picked 100 numbers randomly from the set of natural numbers, what would be the average of them all? But again, show me how you are deriving this probability? Do you suggest that there are more numbers not divisible by 9342193475892734 than there are numbers divisible by 9342193475892734? __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax" Last edited by Robin; 30th July 2018 at 08:08 AM.
 30th July 2018, 08:10 AM #36 Robin Philosopher   Join Date: Apr 2004 Posts: 8,940 Originally Posted by Dave Rogers Seriously, do you think the probability of picking a random integer divisible by ten is equal to the probability of picking one not divisible by ten, and do you think there's more than one way of calculating those probabilities? Dave That is what I am asking, show me your calculation. Are there more numbers not divisible by ten than numbers divisible by ten? __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 30th July 2018, 08:13 AM #37 SOdhner Graduate Poster   Join Date: Apr 2010 Location: Arizona Posts: 1,724 Originally Posted by Robin Are there more numbers not divisible by ten than numbers divisible by ten? There are nine times as many.
 30th July 2018, 08:14 AM #38 Robin Philosopher   Join Date: Apr 2004 Posts: 8,940 Originally Posted by SOdhner There are nine times as many. No there aren't. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 30th July 2018, 08:15 AM #39 SOdhner Graduate Poster   Join Date: Apr 2010 Location: Arizona Posts: 1,724 Originally Posted by Robin No there aren't. Yeah huh.
 30th July 2018, 08:21 AM #40 GlennB Loggerheaded, earth-vexing fustilarian     Join Date: Sep 2006 Location: Arcadia, Greece Posts: 23,293 Originally Posted by Robin I am not sure how you are even proposing to select numbers randomly from an infinite set. If you picked 100 numbers randomly from the set of natural numbers, what would be the average of them all? But again, show me how you are deriving this probability? Do you suggest that there are more numbers not divisible by 9342193475892734 than there are numbers divisible by 9342193475892734? You seem to be relying on the fact that, with an infinite set, there are infinite occurrences of any given number or 'type' of number. While this is true, it doesn't mean the ratio of certain types of number (divisible/not divisible by 9342193475892734 in this case) is the same. Probability calculations depend on that ratio, not the absolute numbers. __________________ "Even a broken clock is right twice a day. 9/11 truth is a clock with no hands." - Beachnut

International Skeptics Forum

 Bookmarks Digg del.icio.us StumbleUpon Google Reddit