just because two things are infinite, doesn't make them equal. Some of them approach infinity at different rates, or are clearly larger or smaller than another
I would like to see some references to different values of infinity please. That is like saying that one is not equal to one for different values of one.
There's a whole wonderful, nasty math of infinities out there for you to do a graduate degree in mathematics on
And I'd really like to hear what the authors of such works would have to say about the whole 1 = 0.999... discussion. After all, this is not new. This discussion was very old and settled when my high school math teacher taught it to me 25 years ago.
Is an infinite number of nines minus an infinite number of nines zero?
Is 0.99999...., minus 0.99999.... equal to zero?
If so, then 9.99999...,
minus 0.99999....
is exactly 9.
You are thinking of a finite number of nines. I'm thinking of an infinite number of nines.
Here is another question for you. What is infinity minue one? An infinite number of nines minus one nine.
In fact, infinity minus one has practical consequence. The Constitution gives Congress the power to grant copyright holders an exclusive right to copy for a limited time. Just some months ago when the whole copyright extension business was in the news, and the Supreme Court was asked to decide whether Congress could extend copyrights this long, our good buddy Jack Valenti (from the Motion Picture Ass. of America) was suggesting that Congress should change the limited time of copyrights to be "Forever minus a day". Maybe we need to get a mathematician to testify before Congress as to what the value of infinity minus one is. Obviously, there are plenty of people, including you, who do not know that it is infinity.
.3 recurring is always going to be a little lower than a third.
No. 0.3333... with some finite number of 3's is going to be less than 1/3.
.3 recurring is exactly equal to 1/3. Exactly. Because the number of trailing 3's is infinite. See the
proof
about 0.9999... recurring being equal to 1.
My excellent high school math teacher had explained to me, when I had asked, exactly what is an irrational number?
Numbers like 1/3, such as 0.3333... are rational, because even though they repeat, such numbers are exactly representable by the ratio of two integers.
In fact, any decimal number that can be expressed as the ratio of two integers, is a rational number. Even a number such as...
0.939287357853918724781923498753298235789
is a rational number. It is just
939287357853918724781923498753298235789 divided by
1000000000000000000000000000000000000000.
Similarly, even a long decimal number, with some trailing set of digits repeating, can be expressed as the ratio of two integers.
An irrational number, such as PI, or the square root of 2, can NOT be expressed as the ratio of two integers.
An easier form of this proof that I used back in 1979 or thereabouts is when arguing with those who don't understand that 0.9999... is equal to 1. I had learned this proof even earlier from my excellent math teacher in high school.
Let x be 0.99999....
x = 0.9999....
10x = 9.9999...
10x - x = 9.9999... - 0.9999... = 9
10x - x = 9 (the infinite trail of nines drop off in the subtraction)
but also, 10x - x = 9x
So, 9x = 9
Therefore x = 1
With this form of the proof, it is easier to see how the trailing nines just drop off in the subtraction. After thinking about this, the key seems to be that after multiplying 0.9999... by ten, to get 9.9999..., you still have the same number (infinity) of nines behind the decimal point.
OpenOffice 1.1RCx produces files that can't be opened by OpenOffice 1.0.
I was not aware of this. Is it possible to provide more detail. I am a heavy OOo user, and write plenty of macros for it. I was not aware of such a case. I would find it interesting to know how to produce a file in 1.1RCx that 1.0.x cannot open.
In either Mozilla or IE 6 on Win XP, it appears to just start the download of an exe file that you can save. Now whether you would want to do this or not is a different question.
Space is awfully expensive. Especially when you say "high power". Wouldn't it be cheaperer to use an unmanned aircraft? Wouldn't it also be betterer, in the following specific ways?
You can launch aircraft and fire the EMP on demand instead of being tied to the fixed orbits of spacecraft. (Or are you also suggesting that spaced based EMP guns also be retaskable?)
Orbits of spacecraft are known to the enemy. (Children, it's time to bring all the EMP sensitive equipment indoors and play.)
lets make A LOT of stuff for them to find! Imagine if all of us created web pages that appeared to hold copywrighted material, but don't. Even just a php or cgi page that generated links with *suspicious words* but nothing of interest
Just be careful of trademark infringement.
Use combinations of words that they are likely to look for such as pac man. Or use the words in ways that are allowed, such as: "My boyfriend drives a Volkswagon while playing pacman." Avoid charged words such as "hates" or "sucks" which might be part of their search pattern. "My friend has less interest in playing pacman than in playing with himself, because the latter is more amusing." No trademark infringement in this last sentence. Just a statement of fact or opinion. (Also don't libel anyone, such as saying "Jane sleeps around".)
I'm not missing or skirting the issue. I understand the issue throughly.
One who writes code holds a copyright on it. You can only use that code if (1) you are granted a license, and (2) you comply with the license.
I pointed out Microsoft's license, Apple's license, Sun's license, and the GPL license. In each case things are the same. You must (1) be granted a license, and (2) comply with the license.
In the case of any of these licenses, if you steal code and put it into your employer's code in breach of any license, then you and your employer will get into trouble. There is nothing here special about the GPL. You should not, ever, under any circumstances, just go copy some code and paste it into your employer's product without a valid license. Ever. This would be true for Microsoft's code, Apple's code, Sun's code, or some GPL code. Whenever your employer uses someone else's IP, your company's legal department should be involved.
With GPL code, I *do* have a licence to use it. Everything released as GPL code comes with a licence for me to use it.
You DO NOT have a license to GPL code unless you (A) agree with and (B) comply with the license. The GPL is very specific about this.
You do not need a license to run a GPL program. There is no EULA to agree to as a condition of running it. Copyright law does not restrict running it. You always need a license to copy anyone's code. (Copyright law applies to copying, not running.) Again, the GPL states that it only applies to copying not running the program.
I am breaking the licence if then I do not release my product under the terms of that licenc however.
You would be infringing the rights of the copyright owner. It is up to the copyright owner to sue you. You do NOT need to make your program GPL. You can settle the suit, pay damages, and cure the infringement. The copyright owner might not be able to proove damages. And as I mentioned earlier, a GPL copyright owner is likely to be easier to settle with in a reasonable fashion than say, Microsoft, if you simply cure the infringement and apologize. Of course, you could also GPL your program, and I'm sure the copyright owner would also be happy.
The SCO case is a bit odd, because they claim that the did not knowingly release the code under the GPL.
They will look pretty silly in court arguing to the judge that they distributed something for eight years without knowing what they were distributing.
They either knew or should have known.
However when they learned of the alledged violation they did not request....
When they learned of the alledged infringement, they have made no attempt to cure it and protect their IP. They are allowing the infringement to continue.
You can't collect damages when you are allowing or even helping the damage to continue.
allowing infringement: not letting anyone cure their infringement, even unintentional violators, such as RedHat or SuSE. These are not cases of willful infringement. I'm sure if the infringement were shown, all of the non-willful parties would be happy to cure the infringement immediately.
helping infringement: continuing to distribute the infringeing code to others to create even more infringement. (i.e. that you can download Linux from SCO.)
The discussion went like this. What happens? Does the program automatically become GPL'ed? Not necessarily. They might just need to cure the copyright infringement, and pay the author any damages. The author may not be able to proove that they have been economically damaged, so in effect, they may only have to cure the copyright violation. There might be other damages for a willful infringement vs. an unintentional infringement. This issue could arise if they then turn around and violate the GPL a second time.
Sorry I can't remember where I read this very interesting discussion. I'm sure it was by someone actually connected with the FSF. It was in connection to some past GPL violation. I think to a violation having to do with a video codec or something like that?
The GPL is not special in any way in regard to this issue.
If you are writing code for your employer, you need to have a clear license to use any code that you get from somewhere else and just copy into your employer's product.
Regardless of where the code comes from. You better have clear license to it in source form. (Or binary form for that matter.) You better have clear license to every single item on that CD you ship. This has always been the case. And here is the real shocker, this has always been the case, even before the GPL existed!
Easy to get ahold of is irrelevant. So if I go to WarezRUs.com and find an easy to get copy of some Microsoft source code, can I later use the excuse that the source was easy to obtain?
SCO, until very recently, made the entire source code to their Unix available for download. Does this mean that you should copy it into your employer's product?
Sun makes Java code available, but NOT under an open source license. What do you think would happen if you used this source in violation of the license?
The moral of this story is, just because you can read or download some source code is no excuse for using it without clear legal title. No matter who it comes from. Code licensed under the GPL has no less of licensing issues than any other code.
The FUD comes in when someone tries to make it sound like the GPL is more of an issue. This is exactly the kind of argument Microsoft was using in their FUD campaign in the spring of 2001.
By only filing four patent infringement counter complaints, IBM doesn't come off in front of the court looking like they're trying to abuse the legal process. Even though they still get the beneficial effect of cutting off all of SCO's revenue.
One things that judges do to help remove any emotion from the argument is to put the shoe on the other foot. Switch the parties to ones that you feel differently about.
When you have to argue with a Microsoftie about the SCO thing, put it this way...
I have code I wrote years ago. Microsoft stole it and put it into Windows. I can't tell you what it is, of course. I'm going to sue Microsoft for infringing my IP. I would also like YOU, Mr. Microsoft user to pay me $1400 for a license to allow you to lawfully use Windows. But since I'm such a nice guy, just like SCO, the introductory price until October is only $666.
Similarly, you sould sell a license to everyone who owns a copy of Brittanica.
anyone who's familiar with IBM's litigation history could'v e told them how unlikely that was
Anyone familiar with IBM's litigation history could also have told them that a patent infringement counter complaint is standard procedure.
Today I finally got around to reading IBM's answer/complaint. When you get to the part about SCO infringing IBM's patents, IBM names which specific products infringe each patent. Now I admit ignorance of SCO's complete product line, but this sounds to me like IBM carefully selected a minimum number of patents, in this case four, that would be infringed by every one of SCO's current or likely products. This has the effect of, if IBM gets an immediate injunction to stop the patent infringement, then this immediately cuts off all revenue for SCO. Additionally, patent infringement suits can only be defended by (1) proving that you don't actually infringe, or (2) prooving that the patent is invalid. Either one is very expensive in terms of the sheer amount of research that has to be done. At this point, on old patents.
Although the patent infringement just sounds like an attempt to be a thorn in the side of SCO, this is likely to kill them. All revenue cut off, and expensive patent lawsuits.
A preliminary injunction on the patents wouldn't cut off the extortion licensing revenue, but IBM's counter complaint also asks for that.
Slashdot Mirror
just because two things are infinite, doesn't make them equal. Some of them approach infinity at different rates, or are clearly larger or smaller than another
I would like to see some references to different values of infinity please. That is like saying that one is not equal to one for different values of one.
There's a whole wonderful, nasty math of infinities out there for you to do a graduate degree in mathematics on
And I'd really like to hear what the authors of such works would have to say about the whole 1 = 0.999... discussion. After all, this is not new. This discussion was very old and settled when my high school math teacher taught it to me 25 years ago.
What miracle?
See this reply I gave earlier.
Is 9.99999... minus 0.9999... exactly equal to nine?
If so, then it must be the case that 9.9999... minus 9 must be exactly equal to 0.9999....
Would you be so kind as to explain how 0.999... is NOT exactly equal to 0.999...?
I think we've all known those things since elementary school as the very definition of rational and irrational.
Good for you. I didn't learn it until high school. In the 70's.
(That is NINTEEN-seventies, in case you were wondering which century.)
I'm not talking about different functions approaching infinity at different rates.
I'm talking about the fact that 9.99999.... minus nine is exactly 0.99999.....
Therefore 9.99999..... minus 0.99999.... must be exactly 9.
Is an infinite number of nines minus an infinite number of nines zero?
Is 0.99999...., minus 0.99999.... equal to zero?
If so, then 9.99999...,
minus 0.99999....
is exactly 9.
You are thinking of a finite number of nines. I'm thinking of an infinite number of nines.
Here is another question for you. What is infinity minue one? An infinite number of nines minus one nine.
In fact, infinity minus one has practical consequence. The Constitution gives Congress the power to grant copyright holders an exclusive right to copy for a limited time. Just some months ago when the whole copyright extension business was in the news, and the Supreme Court was asked to decide whether Congress could extend copyrights this long, our good buddy Jack Valenti (from the Motion Picture Ass. of America) was suggesting that Congress should change the limited time of copyrights to be "Forever minus a day". Maybe we need to get a mathematician to testify before Congress as to what the value of infinity minus one is. Obviously, there are plenty of people, including you, who do not know that it is infinity.
There was a remainder when you divided 1/3 that got thrown out. So your argument is bullshiat.
See this proof .
No. 0.3333... with some finite number of 3's is going to be less than 1/3.
My excellent high school math teacher had explained to me, when I had asked, exactly what is an irrational number?
Numbers like 1/3, such as 0.3333... are rational, because even though they repeat, such numbers are exactly representable by the ratio of two integers.
In fact, any decimal number that can be expressed as the ratio of two integers, is a rational number. Even a number such as...
0.939287357853918724781923498753298235789
is a rational number. It is just
939287357853918724781923498753298235789 divided by 1000000000000000000000000000000000000000.
Similarly, even a long decimal number, with some trailing set of digits repeating, can be expressed as the ratio of two integers.
An irrational number, such as PI, or the square root of 2, can NOT be expressed as the ratio of two integers.
An easier form of this proof that I used back in 1979 or thereabouts is when arguing with those who don't understand that 0.9999... is equal to 1. I had learned this proof even earlier from my excellent math teacher in high school.
Let x be 0.99999....
x = 0.9999....
10x = 9.9999...
10x - x = 9.9999... - 0.9999... = 9
10x - x = 9 (the infinite trail of nines drop off in the subtraction)
but also, 10x - x = 9x
So, 9x = 9
Therefore x = 1
With this form of the proof, it is easier to see how the trailing nines just drop off in the subtraction. After thinking about this, the key seems to be that after multiplying 0.9999... by ten, to get 9.9999..., you still have the same number (infinity) of nines behind the decimal point.
OpenOffice 1.1RCx produces files that can't be opened by OpenOffice 1.0.
I was not aware of this. Is it possible to provide more detail. I am a heavy OOo user, and write plenty of macros for it. I was not aware of such a case. I would find it interesting to know how to produce a file in 1.1RCx that 1.0.x cannot open.
In either Mozilla or IE 6 on Win XP, it appears to just start the download of an exe file that you can save. Now whether you would want to do this or not is a different question.
Slow Down Cowboy!
I wonder if they actually intended for it to sound obscene?
My 10 year old (5th grade) has had an e-mail address for several years.
Space is awfully expensive. Especially when you say "high power". Wouldn't it be cheaperer to use an unmanned aircraft? Wouldn't it also be betterer, in the following specific ways?
But SCO execs are selling their shi.., er, um, I meant, selling their stock. Not flushing it.
and who is going to pay for 240 years of retirement?
I think you are overly optimistic. Corporations will find some way to work us to their advantage.
where are all these people going to live, what are they going to eat
And what makes you think that so many people will get this privilege? Last time I checked, the peon to CEO ratio is very high.
lets make A LOT of stuff for them to find! Imagine if all of us created web pages that appeared to hold copywrighted material, but don't. Even just a php or cgi page that generated links with *suspicious words* but nothing of interest
Just be careful of trademark infringement.
Use combinations of words that they are likely to look for such as pac man. Or use the words in ways that are allowed, such as: "My boyfriend drives a Volkswagon while playing pacman." Avoid charged words such as "hates" or "sucks" which might be part of their search pattern. "My friend has less interest in playing pacman than in playing with himself, because the latter is more amusing." No trademark infringement in this last sentence. Just a statement of fact or opinion. (Also don't libel anyone, such as saying "Jane sleeps around".)
I'm not missing or skirting the issue. I understand the issue throughly.
One who writes code holds a copyright on it. You can only use that code if (1) you are granted a license, and (2) you comply with the license.
I pointed out Microsoft's license, Apple's license, Sun's license, and the GPL license. In each case things are the same. You must (1) be granted a license, and (2) comply with the license.
In the case of any of these licenses, if you steal code and put it into your employer's code in breach of any license, then you and your employer will get into trouble. There is nothing here special about the GPL. You should not, ever, under any circumstances, just go copy some code and paste it into your employer's product without a valid license. Ever. This would be true for Microsoft's code, Apple's code, Sun's code, or some GPL code. Whenever your employer uses someone else's IP, your company's legal department should be involved.
With GPL code, I *do* have a licence to use it. Everything released as GPL code comes with a licence for me to use it.
You DO NOT have a license to GPL code unless you (A) agree with and (B) comply with the license. The GPL is very specific about this.
You do not need a license to run a GPL program. There is no EULA to agree to as a condition of running it. Copyright law does not restrict running it. You always need a license to copy anyone's code. (Copyright law applies to copying, not running.) Again, the GPL states that it only applies to copying not running the program.
I am breaking the licence if then I do not release my product under the terms of that licenc however.
You would be infringing the rights of the copyright owner. It is up to the copyright owner to sue you. You do NOT need to make your program GPL. You can settle the suit, pay damages, and cure the infringement. The copyright owner might not be able to proove damages. And as I mentioned earlier, a GPL copyright owner is likely to be easier to settle with in a reasonable fashion than say, Microsoft, if you simply cure the infringement and apologize. Of course, you could also GPL your program, and I'm sure the copyright owner would also be happy.
They will look pretty silly in court arguing to the judge that they distributed something for eight years without knowing what they were distributing.
They either knew or should have known.
However when they learned of the alledged violation they did not request....
When they learned of the alledged infringement, they have made no attempt to cure it and protect their IP. They are allowing the infringement to continue.
You can't collect damages when you are allowing or even helping the damage to continue.
Interesting... Can you point to a link?
No, I cannot find one.
I read extensively about this topic in the past.
The discussion went like this. What happens? Does the program automatically become GPL'ed? Not necessarily. They might just need to cure the copyright infringement, and pay the author any damages. The author may not be able to proove that they have been economically damaged, so in effect, they may only have to cure the copyright violation. There might be other damages for a willful infringement vs. an unintentional infringement. This issue could arise if they then turn around and violate the GPL a second time.
Sorry I can't remember where I read this very interesting discussion. I'm sure it was by someone actually connected with the FSF. It was in connection to some past GPL violation. I think to a violation having to do with a video codec or something like that?
That is irrelevant.
See this post for my argument.
The GPL is not special in any way in regard to this issue.
If you are writing code for your employer, you need to have a clear license to use any code that you get from somewhere else and just copy into your employer's product.
Regardless of where the code comes from. You better have clear license to it in source form. (Or binary form for that matter.) You better have clear license to every single item on that CD you ship. This has always been the case. And here is the real shocker, this has always been the case, even before the GPL existed!
Easy to get ahold of is irrelevant. So if I go to WarezRUs.com and find an easy to get copy of some Microsoft source code, can I later use the excuse that the source was easy to obtain?
SCO, until very recently, made the entire source code to their Unix available for download. Does this mean that you should copy it into your employer's product?
Sun makes Java code available, but NOT under an open source license. What do you think would happen if you used this source in violation of the license?
The moral of this story is, just because you can read or download some source code is no excuse for using it without clear legal title. No matter who it comes from. Code licensed under the GPL has no less of licensing issues than any other code.
The FUD comes in when someone tries to make it sound like the GPL is more of an issue. This is exactly the kind of argument Microsoft was using in their FUD campaign in the spring of 2001.
By only filing four patent infringement counter complaints, IBM doesn't come off in front of the court looking like they're trying to abuse the legal process. Even though they still get the beneficial effect of cutting off all of SCO's revenue.
One things that judges do to help remove any emotion from the argument is to put the shoe on the other foot. Switch the parties to ones that you feel differently about.
When you have to argue with a Microsoftie about the SCO thing, put it this way...
I have code I wrote years ago. Microsoft stole it and put it into Windows. I can't tell you what it is, of course. I'm going to sue Microsoft for infringing my IP. I would also like YOU, Mr. Microsoft user to pay me $1400 for a license to allow you to lawfully use Windows. But since I'm such a nice guy, just like SCO, the introductory price until October is only $666.
Similarly, you sould sell a license to everyone who owns a copy of Brittanica.
anyone who's familiar with IBM's litigation history could'v e told them how unlikely that was
Anyone familiar with IBM's litigation history could also have told them that a patent infringement counter complaint is standard procedure.
Today I finally got around to reading IBM's answer/complaint. When you get to the part about SCO infringing IBM's patents, IBM names which specific products infringe each patent. Now I admit ignorance of SCO's complete product line, but this sounds to me like IBM carefully selected a minimum number of patents, in this case four, that would be infringed by every one of SCO's current or likely products. This has the effect of, if IBM gets an immediate injunction to stop the patent infringement, then this immediately cuts off all revenue for SCO. Additionally, patent infringement suits can only be defended by (1) proving that you don't actually infringe, or (2) prooving that the patent is invalid. Either one is very expensive in terms of the sheer amount of research that has to be done. At this point, on old patents.
Although the patent infringement just sounds like an attempt to be a thorn in the side of SCO, this is likely to kill them. All revenue cut off, and expensive patent lawsuits.
A preliminary injunction on the patents wouldn't cut off the extortion licensing revenue, but IBM's counter complaint also asks for that.