I wouldn't say a dictionary is really a governing body. Moreso, the one you link just scrapes web results and is pulling them from "The Free On-Line Dictionary of Computing" and "The Jargon File", the former of which is useful, but not really an authority of any form and the latter of which is specifically, by its own admission, full of definitions in as far as they are used by "hackers".
The more commonly understood definition is a license that meets the Open Source Definition [opensource.org], which MS-LPL obviously does not (contravenes point 10 at least).
More commonly understood by whom? I bet you I could take 10 random people who know the term off the street and at least 9 of them would say "you can see the source code" or something similar to that. Hell, even here at Harvey Mudd College I could probably get at least 7 or 8 people out of 10 say the same.
I don't know about anyone else, but since the first time I heard the term "open source", I've always thought of the source being open to view./Maybe/ open to modification, but not necessarily. Anything above and beyond is gravy until you reach Free/Libre software (initial capitalization important here).
At some point I learned of the OSI's Open Source, but I have *never* equated it plain open source.
I'm not sure how closely you read the article on constructivism, but if you're trying to relate it to the discussion about infinite cardinalities or your "set with time" concept you kept hinting at, it doesn't really help argue your case and, in fact, comes down on our side.
On the other hand, if you're pointing to the part where they are throwing out an axiom and saying you're doing similar, that's great. All the same, they're throwing out an axiom that doesn't jive with them, telling us which it is, and getting useful results out of it (ish). Of course, I'm also of the opinion that intuitionist logic (and by extension mathematical constructivism) is a load of BS outside of areas like typed lambda calculus, and even then I call limited use.
I must say, though, it is good of you to stick around in this discussion and, hopefully, learn something (whether you like it or not) rather than say "well, I'm right and you're wrong and I'm done arguing about it". If you don't mind my asking, though, where do you stand, age/education/mathematical training-wise. I ask this, not to dismiss you in any way, but more to get a better idea of how to talk to you from here on out in this regard.
These two other gentlemen seem to have addressed your other points satisfactorily enough that I won't comment on them unless you specifically ask me to.
That said, there's a reason that our reasoning assumes time is not a factor: it isn't. There is no notion of time in a set. A set is a collection of things there and time has no place in sets. If you want to factor in time, however you wish to do so, then we aren't talking about sets anymore, so we aren't talking about cardinalities, and we aren't talking about "degrees of infinity". You tell me that I brought cardinality into this discussion but you were the one who began talking about sets of things and cardinalities of those sets in your first post (implicitly, granted, but it's the only construct that made sense in the context).
Further, if you are attempting to invent a new construct here, please define it for us. Tell us what gap in mathematical reasoning, rather than your own desire, is missing and how your new construct fills that gap. Tell us why we care about this new construct other than that "it feels good".
You'll note that this property that you quote is one I listed as an important distinguishing feature of infinite set that makes these seemingly impossible truths possible.
Just because a proper subset has the same cardinality doesn't mean information is lost. Again, the fact the map from the one set to the other is a bijection means there's a map from the other set to the one, restoring the first set. Given either set and the bijection, you *have* the other set regardless, so no information is lost.
Sets have no notion of "growing to infinity" or the "speed" at which they do so. They are simply collections of things. And there are as many things in the set of all primes as there are in the set of all natural numbers. The reals have a higher cardinality than the set of naturals, not because they "grow to infinity" faster or anything silly like that, but because there are simply more of them there.
And, yes, I agree aleph_1 > aleph_0. I don't agree that in my bijection that the primes grow faster, though I will agree that the nth prime will be larger than the n-1th by more than n in general. But the important thing is that they're not really "growing to an infinity" because infinity isn't a number (even if we do say infinite number, it's more a convenience of ambiguous terminology than anything).
And, even more importantly, the cardinality of a set isn't what it "grows to" as you keep saying, as that doesn't even make sense.
If you allow me a small aside on how that doesn't make sense, it will become clear. Firstly, for your notion to make sense, we would have to say that |{2,3,4,5}| = 5 since it clearly "grows to" 5 in your words, but we should be able to see that |{2,3,4,5}| = 4. Cardinality is a measure of how many things are in a set not how large are the things in the set.
Another, hopefully illuminating, related bit: take the sets of the first n natural numbers and the first n prime numbers. Say, n=5, so we have N_5 = {1,2,3,4,5} and p_5 = {2,3,5,7,11}. Surely we can both agree that the cardinality of both of these is 5 and the fact that the set of primes "grows faster" doesn't change that. All that we care about is *how many things are in it*.
You are correct in that the choice of 0 to begin with isn't necessary, but it is convenient because we do need some manner of ordering them algorithmically. Another possible ordering that fulfills order is {6, 2, 5, 0, 1, -2, -1, 3, -3, 4, -4, -5, -6, 7, -7, 8, -8, 9, -9,...}.
I have to admit, you've lost me with this post. To begin with, I can't make much sense of your geometric description or how my (admittedly rushed and slightly handwaved, though there exist far more formal and robust forms of them) proofs hinged on it. The proofs I used hinged on one of the basic principles underlying a very rich and important field, combinatorics. This principle is that the ability to create a bijection between two sets implies equal cardinality and the provable inability to do so implies unequal cardinality. Further, the simple fact that there exists these bijections means that no information is being lost. As long as you have one set and a bijection between it and another set, you have that second set and all the information it contains.
Cardinality is not an artificial construct. It's a measure of how many things there are. It's easy to see |{1,2,3}| = |{cat, bird, dog}| = 3 and that there's nothing artificial about this. Your issue is with the extension into the infinite, which is perfectly understandable since infinity is a pretty abstract and difficult concept. Thing is, it's a very real and very useful concept, so we're not ditching it any time soon.
Consider the history of mathematics: natural numbers are a given. I mean, as soon as you have a concept of "how many" in any way (which is a pretty basic concept", the natural numbers quickly follow. Even fractions are relatively intuitive, as you can have a pie and cut it into two pieces. It is obvious that neither piece is a pie, but that both together are, so we have 1/2. Then we get the concept of 0. How can nothing be a number? Then we introduce the concept of negative numbers. Negative numbers were considered absurd and meaningless until very recently. Hell, Euler believed negative numbers to be greater than infinity and therefore safely ignored. Irrationals were accepted a long time ago, but they caused a lot of unrest when it was first proved that there exist some numbers that are not rational. As it turns out, they are labeled "irrational" because they were thought to make no sense. In a similar vein, the imaginary numbers were named as such by Descartes because they clearly could not be possible, yet they are important in many applications today. Fortunately, people were far more willing to accept the quaternions (a four-dimensional non-commutative extension of the complex numbers) and the octonions (an eight-dimensional non-associative extension of the quaternions), but I'm willing to be that the concepts of these two still boggle your mind (took me a while to get used to them, anyway).
Infinity, and the different cardinalities therein, are kind of the same way as all of these numerical extensions with the being non-intuitive, but still correct and useful. There is no need to really get a new definition of cardinality given that the one we have works for everything we know and provides useful results. Much like with the irrationals, the negatives, the complex, etc, it's a useful concept that one needs to learn to adjust to and it will make a lot more sense. Intuition, as it turns out, does need some training to be useful.
Also, I don't get your last sentence or in what way I depended on zero....
It is rather counterintuitive, actually. The mathematicians of the time were rather upset by Cantor's results and it took some time before this notion was widely accepted. I don't know what you mean by "precise", but if you mean what I think you do (and that I'm having difficulty explaining without misusing other mathematical terms, and thus won't), I'd say cardinality is precisely defined.
A quick lesson:
We start with the natural numbers, N = {0, 1, 2, 3, 4, 5,...} and we see it has cardinality aleph null. Now, hopefully you can see, even if you can't see why, that the set {1, 2, 3, 4, 5, 6,.....} has the same cardinality as N despite missing the 0. In fact, one of the defining features of an infinite set is the ability to have a proper subset (that is, a subset that isn't the entire set) with the same cardinality as the entire set.
Now, the first surprising result: the integers, Z={..., -3, -2, -1, 0, 1, 2, 3,...}, have the same cardinality as N. We can show this using one of the basic principles of combinatorics: if you can create a bijection between the members of two sets, their cardinalities are equal.
(This paragraph is defining a bijection. If you are familiar with that, feel free to skip this). A bijection, if you don't know, is a map from one set to another such that the map is both injective and surjective. A map simply associates a member of the first set to a member of the set you are mapping it to through some method or another (for example, f(x) = x+1 is a map from the reals to the reals (f:R->R) such that the member x is associated with the member x+1). A map is injective if distinct members from the first set map to distinct members of the second set or, equivalently, that if two members map to the same thing, those members must be equal. A map is surjective if everything in the second set gets mapped to.
Now, to show that |Z| = |N| (Z has the same cardinality as N) we must find a bijection between them. The easiest way to do this is to find a systematic way that would list all of the members of Z given an infinite amount of time. Clearly {..., -3, -2, -1, 0, 1, 2, 3,...} won't work since it is unbounded on both sides. However, it should be easy to see that {0, 1, -1, 2, -2, 3, -3,...} should be work just fine, and our bijection would be that the nth member of the set would map to the nth natural number. Thus, |Z|=|N|.
Now, this probably doesn't shock and amaze much anymore. But one that still continues to be amazing is that the rational numbers, Q={1, 1/2, 1/3, 1/4, -1, -1/2, -6/7, 3,...}, have the same cardinality as the integers. The proof of this one is a little difficult to show in a slashdot comment, but the idea is to make a grid with numerators running across the x-axis and denominators running across the y-axis. Thus the top row would be all the members of N (the proof is easier to show using only positive numerators/denominators, but you can hopefully see from the previous example how you can throw the negatives in). If we then start with the top left-most entry (1/1=1), we can start reading off diagonals, giving us a listing like {1, 2, 1/2, 1/3, 1, 3,...}. You'll note that we have a duplicate in this set, but it is trivial to simply skip over duplicate entries, so we can do so without affecting the cardinality. This creates a bijection between Q and N (well, technically between Q+ and N, but again, you can see how we can add in Q- and 0 trivially).
Now, having shown that |N|=|Z|=|Q|, one might think that maybe |R|=|N| (where R is the reals). Cantor further showed that this isn't true. In fact, |[0,1]| > |N| (that is, the cardinality of the reals between 0 and 1 is greater than the cardinality of the natural numbers). Again, this one is easier to show given something to draw on, but I'll make do. Assume you can list all of the reals between 0 and 1. Just make an infinite list of as ma
As the AC said, the integers and the primes have the same cardinality, but you could use the integers and the reals, or the integers and the powerset of the integers or the rationals and the reals or all sorts or many, many, other examples. Just a bad choice with that one, though.
And you really should have known that binding the context too quickly would have made you look like a dolt. If you read the link you will see that the FSF was being held as an authority on the GPL (as it tends to be) and the decision it gave was to be held as correct, which fits under any reasonable definition of 'rule'.
It's not even a far-fetched alternate definition, either. While they may not be a *legal* authority per se, their ruling is often taken to be as good as law when it comes to interpretations of the GPL.
Now, whether this example was particularly relevant to the discussion (as the GPL and CC are not the same and, unless something happened I haven't been told of, the FSF isn't CC) is a completely different issue, but word usage was just fine here.
Oh, and as a final note: if you're going to make a really bad analogy, please stick to cars.
As long as they're considered any form of authority (which many do when it comes to OSS, for what I hope are obvious reasons), they can certainly rule on it. It doesn't mean that what they say is *legally binding*, but it does mean the people are likely to respect what they decide.
I realize feeding the trolls is a bad idea, but as a Mudder myself, I'd hate for the casual reader to get the wrong idea about us from the AC. Mudd is a liberal arts school with a strong humanities & social science emphasis in addition to all of the thermionic emissions and np completeness stuff. If you want to call English and religious studies (the latter of which I'm concentrating in) 'fluff', then, yeah, Mudd is about 'fluff'.
Third, RACIST? What the hell? Can you PLEASE explain that, because I REALLY don't get that one. Honestly, I haven't a clue where you got that and really want to know.
Well, he got it from http://en.wikipedia.org/wiki/Michael_Richards#Laugh_Factory_incident. Incidentally, I think the racism claim may be a little strong here, since the given explanation is actually pretty plausible (before you dispute it, I would like to point out that most people on/b/ are not *actually* racist).
Not buying it because of SecuROM is certainly NOT justified, for many reasons.
Firstly, while I'm opposed to copy protection of this flavour in general, SecuROM is one of the tamer options out there. Yes, it causes problems for some users, but really, there's far worse out there. For instance, the horror that is StarForce. That's an example of a copy protection that crosses the line so blatantly, that it would be justified to all-out refuse to buy the game. SecuROM has if anything improved recently, notably, the v.7.x series can install and run in a non-administrator account, which has obvious security and stability benefits.
I will admit to not being 100% sure about the technical details in this regard, but is the 3-activation limit part of SecuROM? If so, you are so very wrong. If not, you may be correct (I disagree, having experienced SecuROM problems in the past, but I do not know the numbers at large), but there is a related, *very* justified reason in this ridiculous restriction.
No. A loan is receiving a lump sum of money now (sometimes more than you can gather yourself, sometimes just more convenient to get a loan for) and then paying it back (plus interest, of course) over the course of some time frame. Affording it means being able to pay it back by the established time limit (or earlier!) while maintaining financial security otherwise.
You were clearly replying to my post (being that it's, well, a reply to my post). The only bit of my post that your reply makes any sense as a response to is the "legitimate service" part, but legitimate doesn't strictly mean legal, the "illegal service" comment is irrelevant. The rest of your post shows the way it *is* but since I was arguing the way it *should be*, that's also irrelevant.
What is is it with slashdotters and selective quoting. That sentence actually reads
The legality of the issue is totally peripheral to whether it is constructive or not.
Legality may have been the original topic (I still don't believe it was, but no matter), but this thread, at least, branched off from that into "constructiveness".
So you claim that not a single Adobe Photoshop has ever been pirated on a system instead of being payed for?
No. I don't even know how that could be inferred from what I wrote.
I'm on your side in this one, but I inferred the same since you were arguing against the point that piracy leads to reduced profits from the case where nobody pirates. The only way for profits not to be less than the case of no piracy is if everyone who pirates it would not have bought it OR everyone who pirates it that would have bought it convinces somebody to buy it that otherwise wouldn't have. It's a reasonable inferrence, really.
Out of curiosity (not that I expect you to actually come back and read this), what distro are you running, because I have Flash running on 64-bit lenny thanks to a compatibility package.
Slashdot Mirror
I wouldn't say a dictionary is really a governing body. Moreso, the one you link just scrapes web results and is pulling them from "The Free On-Line Dictionary of Computing" and "The Jargon File", the former of which is useful, but not really an authority of any form and the latter of which is specifically, by its own admission, full of definitions in as far as they are used by "hackers".
The more commonly understood definition is a license that meets the Open Source Definition [opensource.org], which MS-LPL obviously does not (contravenes point 10 at least).
More commonly understood by whom? I bet you I could take 10 random people who know the term off the street and at least 9 of them would say "you can see the source code" or something similar to that. Hell, even here at Harvey Mudd College I could probably get at least 7 or 8 people out of 10 say the same.
From your link:
OSI is registering the Open Source Initiative Approved License trademark
That is *not* the same thing as trademarking "open source" or even "Open Source". IIRC, they tried and it wasn't granted....
Only if you show me where in copyright law that compiling code is a right that can be reserved.
Awesome! I'm personally anti-life!
I don't know about anyone else, but since the first time I heard the term "open source", I've always thought of the source being open to view. /Maybe/ open to modification, but not necessarily. Anything above and beyond is gravy until you reach Free/Libre software (initial capitalization important here).
At some point I learned of the OSI's Open Source, but I have *never* equated it plain open source.
I'm not sure how closely you read the article on constructivism, but if you're trying to relate it to the discussion about infinite cardinalities or your "set with time" concept you kept hinting at, it doesn't really help argue your case and, in fact, comes down on our side.
On the other hand, if you're pointing to the part where they are throwing out an axiom and saying you're doing similar, that's great. All the same, they're throwing out an axiom that doesn't jive with them, telling us which it is, and getting useful results out of it (ish). Of course, I'm also of the opinion that intuitionist logic (and by extension mathematical constructivism) is a load of BS outside of areas like typed lambda calculus, and even then I call limited use.
I must say, though, it is good of you to stick around in this discussion and, hopefully, learn something (whether you like it or not) rather than say "well, I'm right and you're wrong and I'm done arguing about it". If you don't mind my asking, though, where do you stand, age/education/mathematical training-wise. I ask this, not to dismiss you in any way, but more to get a better idea of how to talk to you from here on out in this regard.
These two other gentlemen seem to have addressed your other points satisfactorily enough that I won't comment on them unless you specifically ask me to.
That said, there's a reason that our reasoning assumes time is not a factor: it isn't. There is no notion of time in a set. A set is a collection of things there and time has no place in sets. If you want to factor in time, however you wish to do so, then we aren't talking about sets anymore, so we aren't talking about cardinalities, and we aren't talking about "degrees of infinity". You tell me that I brought cardinality into this discussion but you were the one who began talking about sets of things and cardinalities of those sets in your first post (implicitly, granted, but it's the only construct that made sense in the context).
Further, if you are attempting to invent a new construct here, please define it for us. Tell us what gap in mathematical reasoning, rather than your own desire, is missing and how your new construct fills that gap. Tell us why we care about this new construct other than that "it feels good".
You'll note that this property that you quote is one I listed as an important distinguishing feature of infinite set that makes these seemingly impossible truths possible.
Just because a proper subset has the same cardinality doesn't mean information is lost. Again, the fact the map from the one set to the other is a bijection means there's a map from the other set to the one, restoring the first set. Given either set and the bijection, you *have* the other set regardless, so no information is lost.
Sets have no notion of "growing to infinity" or the "speed" at which they do so. They are simply collections of things. And there are as many things in the set of all primes as there are in the set of all natural numbers. The reals have a higher cardinality than the set of naturals, not because they "grow to infinity" faster or anything silly like that, but because there are simply more of them there.
And, yes, I agree aleph_1 > aleph_0. I don't agree that in my bijection that the primes grow faster, though I will agree that the nth prime will be larger than the n-1th by more than n in general. But the important thing is that they're not really "growing to an infinity" because infinity isn't a number (even if we do say infinite number, it's more a convenience of ambiguous terminology than anything).
And, even more importantly, the cardinality of a set isn't what it "grows to" as you keep saying, as that doesn't even make sense.
If you allow me a small aside on how that doesn't make sense, it will become clear. Firstly, for your notion to make sense, we would have to say that |{2,3,4,5}| = 5 since it clearly "grows to" 5 in your words, but we should be able to see that |{2,3,4,5}| = 4. Cardinality is a measure of how many things are in a set not how large are the things in the set.
Another, hopefully illuminating, related bit: take the sets of the first n natural numbers and the first n prime numbers. Say, n=5, so we have N_5 = {1,2,3,4,5} and p_5 = {2,3,5,7,11}. Surely we can both agree that the cardinality of both of these is 5 and the fact that the set of primes "grows faster" doesn't change that. All that we care about is *how many things are in it*.
You are correct in that the choice of 0 to begin with isn't necessary, but it is convenient because we do need some manner of ordering them algorithmically. Another possible ordering that fulfills order is {6, 2, 5, 0, 1, -2, -1, 3, -3, 4, -4, -5, -6, 7, -7, 8, -8, 9, -9, ...}.
I have to admit, you've lost me with this post. To begin with, I can't make much sense of your geometric description or how my (admittedly rushed and slightly handwaved, though there exist far more formal and robust forms of them) proofs hinged on it. The proofs I used hinged on one of the basic principles underlying a very rich and important field, combinatorics. This principle is that the ability to create a bijection between two sets implies equal cardinality and the provable inability to do so implies unequal cardinality. Further, the simple fact that there exists these bijections means that no information is being lost. As long as you have one set and a bijection between it and another set, you have that second set and all the information it contains.
Cardinality is not an artificial construct. It's a measure of how many things there are. It's easy to see |{1,2,3}| = |{cat, bird, dog}| = 3 and that there's nothing artificial about this. Your issue is with the extension into the infinite, which is perfectly understandable since infinity is a pretty abstract and difficult concept. Thing is, it's a very real and very useful concept, so we're not ditching it any time soon.
Consider the history of mathematics: natural numbers are a given. I mean, as soon as you have a concept of "how many" in any way (which is a pretty basic concept", the natural numbers quickly follow. Even fractions are relatively intuitive, as you can have a pie and cut it into two pieces. It is obvious that neither piece is a pie, but that both together are, so we have 1/2. Then we get the concept of 0. How can nothing be a number? Then we introduce the concept of negative numbers. Negative numbers were considered absurd and meaningless until very recently. Hell, Euler believed negative numbers to be greater than infinity and therefore safely ignored. Irrationals were accepted a long time ago, but they caused a lot of unrest when it was first proved that there exist some numbers that are not rational. As it turns out, they are labeled "irrational" because they were thought to make no sense. In a similar vein, the imaginary numbers were named as such by Descartes because they clearly could not be possible, yet they are important in many applications today. Fortunately, people were far more willing to accept the quaternions (a four-dimensional non-commutative extension of the complex numbers) and the octonions (an eight-dimensional non-associative extension of the quaternions), but I'm willing to be that the concepts of these two still boggle your mind (took me a while to get used to them, anyway).
Infinity, and the different cardinalities therein, are kind of the same way as all of these numerical extensions with the being non-intuitive, but still correct and useful. There is no need to really get a new definition of cardinality given that the one we have works for everything we know and provides useful results. Much like with the irrationals, the negatives, the complex, etc, it's a useful concept that one needs to learn to adjust to and it will make a lot more sense. Intuition, as it turns out, does need some training to be useful.
Also, I don't get your last sentence or in what way I depended on zero....
It is rather counterintuitive, actually. The mathematicians of the time were rather upset by Cantor's results and it took some time before this notion was widely accepted. I don't know what you mean by "precise", but if you mean what I think you do (and that I'm having difficulty explaining without misusing other mathematical terms, and thus won't), I'd say cardinality is precisely defined.
A quick lesson:
We start with the natural numbers, N = {0, 1, 2, 3, 4, 5, ...} and we see it has cardinality aleph null. Now, hopefully you can see, even if you can't see why, that the set {1, 2, 3, 4, 5, 6, .....} has the same cardinality as N despite missing the 0. In fact, one of the defining features of an infinite set is the ability to have a proper subset (that is, a subset that isn't the entire set) with the same cardinality as the entire set.
Now, the first surprising result: the integers, Z={..., -3, -2, -1, 0, 1, 2, 3, ...}, have the same cardinality as N. We can show this using one of the basic principles of combinatorics: if you can create a bijection between the members of two sets, their cardinalities are equal.
(This paragraph is defining a bijection. If you are familiar with that, feel free to skip this). A bijection, if you don't know, is a map from one set to another such that the map is both injective and surjective. A map simply associates a member of the first set to a member of the set you are mapping it to through some method or another (for example, f(x) = x+1 is a map from the reals to the reals (f:R->R) such that the member x is associated with the member x+1). A map is injective if distinct members from the first set map to distinct members of the second set or, equivalently, that if two members map to the same thing, those members must be equal. A map is surjective if everything in the second set gets mapped to.
Now, to show that |Z| = |N| (Z has the same cardinality as N) we must find a bijection between them. The easiest way to do this is to find a systematic way that would list all of the members of Z given an infinite amount of time. Clearly {..., -3, -2, -1, 0, 1, 2, 3, ...} won't work since it is unbounded on both sides. However, it should be easy to see that {0, 1, -1, 2, -2, 3, -3, ...} should be work just fine, and our bijection would be that the nth member of the set would map to the nth natural number. Thus, |Z|=|N|.
Now, this probably doesn't shock and amaze much anymore. But one that still continues to be amazing is that the rational numbers, Q={1, 1/2, 1/3, 1/4, -1, -1/2, -6/7, 3, ...}, have the same cardinality as the integers. The proof of this one is a little difficult to show in a slashdot comment, but the idea is to make a grid with numerators running across the x-axis and denominators running across the y-axis. Thus the top row would be all the members of N (the proof is easier to show using only positive numerators/denominators, but you can hopefully see from the previous example how you can throw the negatives in). If we then start with the top left-most entry (1/1=1), we can start reading off diagonals, giving us a listing like {1, 2, 1/2, 1/3, 1, 3, ...}. You'll note that we have a duplicate in this set, but it is trivial to simply skip over duplicate entries, so we can do so without affecting the cardinality. This creates a bijection between Q and N (well, technically between Q+ and N, but again, you can see how we can add in Q- and 0 trivially).
Now, having shown that |N|=|Z|=|Q|, one might think that maybe |R|=|N| (where R is the reals). Cantor further showed that this isn't true. In fact, |[0,1]| > |N| (that is, the cardinality of the reals between 0 and 1 is greater than the cardinality of the natural numbers). Again, this one is easier to show given something to draw on, but I'll make do. Assume you can list all of the reals between 0 and 1. Just make an infinite list of as ma
Well-played, sir.
As the AC said, the integers and the primes have the same cardinality, but you could use the integers and the reals, or the integers and the powerset of the integers or the rationals and the reals or all sorts or many, many, other examples. Just a bad choice with that one, though.
And you really should have known that binding the context too quickly would have made you look like a dolt. If you read the link you will see that the FSF was being held as an authority on the GPL (as it tends to be) and the decision it gave was to be held as correct, which fits under any reasonable definition of 'rule'.
It's not even a far-fetched alternate definition, either. While they may not be a *legal* authority per se, their ruling is often taken to be as good as law when it comes to interpretations of the GPL.
Now, whether this example was particularly relevant to the discussion (as the GPL and CC are not the same and, unless something happened I haven't been told of, the FSF isn't CC) is a completely different issue, but word usage was just fine here.
Oh, and as a final note: if you're going to make a really bad analogy, please stick to cars.
As long as they're considered any form of authority (which many do when it comes to OSS, for what I hope are obvious reasons), they can certainly rule on it. It doesn't mean that what they say is *legally binding*, but it does mean the people are likely to respect what they decide.
I realize feeding the trolls is a bad idea, but as a Mudder myself, I'd hate for the casual reader to get the wrong idea about us from the AC. Mudd is a liberal arts school with a strong humanities & social science emphasis in addition to all of the thermionic emissions and np completeness stuff. If you want to call English and religious studies (the latter of which I'm concentrating in) 'fluff', then, yeah, Mudd is about 'fluff'.
Third, RACIST? What the hell? Can you PLEASE explain that, because I REALLY don't get that one. Honestly, I haven't a clue where you got that and really want to know.
Well, he got it from http://en.wikipedia.org/wiki/Michael_Richards#Laugh_Factory_incident. Incidentally, I think the racism claim may be a little strong here, since the given explanation is actually pretty plausible (before you dispute it, I would like to point out that most people on /b/ are not *actually* racist).
Not buying it because of SecuROM is certainly NOT justified, for many reasons. Firstly, while I'm opposed to copy protection of this flavour in general, SecuROM is one of the tamer options out there. Yes, it causes problems for some users, but really, there's far worse out there. For instance, the horror that is StarForce. That's an example of a copy protection that crosses the line so blatantly, that it would be justified to all-out refuse to buy the game. SecuROM has if anything improved recently, notably, the v.7.x series can install and run in a non-administrator account, which has obvious security and stability benefits.
I will admit to not being 100% sure about the technical details in this regard, but is the 3-activation limit part of SecuROM? If so, you are so very wrong. If not, you may be correct (I disagree, having experienced SecuROM problems in the past, but I do not know the numbers at large), but there is a related, *very* justified reason in this ridiculous restriction.
No. A loan is receiving a lump sum of money now (sometimes more than you can gather yourself, sometimes just more convenient to get a loan for) and then paying it back (plus interest, of course) over the course of some time frame. Affording it means being able to pay it back by the established time limit (or earlier!) while maintaining financial security otherwise.
You were clearly replying to my post (being that it's, well, a reply to my post). The only bit of my post that your reply makes any sense as a response to is the "legitimate service" part, but legitimate doesn't strictly mean legal, the "illegal service" comment is irrelevant. The rest of your post shows the way it *is* but since I was arguing the way it *should be*, that's also irrelevant.
I liked the movie, too, but it wasn't Hellblazer by any means.
The legality of the issue is totally peripheral to whether it is constructive or not.
Legality may have been the original topic (I still don't believe it was, but no matter), but this thread, at least, branched off from that into "constructiveness".
So you claim that not a single Adobe Photoshop has ever been pirated on a system instead of being payed for? No. I don't even know how that could be inferred from what I wrote.
I'm on your side in this one, but I inferred the same since you were arguing against the point that piracy leads to reduced profits from the case where nobody pirates. The only way for profits not to be less than the case of no piracy is if everyone who pirates it would not have bought it OR everyone who pirates it that would have bought it convinces somebody to buy it that otherwise wouldn't have. It's a reasonable inferrence, really.
Out of curiosity (not that I expect you to actually come back and read this), what distro are you running, because I have Flash running on 64-bit lenny thanks to a compatibility package.