I'm going to try to give an example of Cantor's diagonalization method, to show that we can create a set which is "bigger" than the set of natural numbers.
Consider the set N, the set of natural numbers and the set X, where X is the set of all infinite binary sequences (i.e. all sequences {a(n),n=0..infinity|a(n) = 0 or 1}
Let's assume we can do a "1 to 1" correspondance between these two sets. If we can, we can find a function f(n) which when applied to the natural numbers will give f(1), f(2), f(3), and supposedly this will generate all members of X.
Let me create a new binary sequence that is not covered by that mapping.
Here is how I am going to create my sequence. For the first number in my sequence, I'm going to look at whatever f(1) is. Maybe it's {0,1,1,1,1,...} whatever. Whatever f(1) has as it's first number, I'm going to use the other number (0 if 1, 1 if 0), as the first number of my new sequence. For the second number of my new sequence, I'm going to look at f(2), and the number in it's second position, and again, use the "other number".
For the third number in my sequence I'm going to use the "other" number than the third number in f(3), etc.... So for each position f(n), I will use the "other" number than the nth number in f(n).
What this gives me is a sequence that is guaranteed to be different than every f(n) sequence, because the number in position n is different.
Thus I have a new sequence. But this is supposedly impossible, because f(1), f(2), f(3) was supposed to be every sequence.
Thus, no function f exists. Thus this set X can not be put in a 1 to 1 correspondance with the natural numbers. Hope that helps.
The obvious point to this message is to note that the RIAA and MPAA are in different situations. The music industry is seeing a SHARP DECLINE in revenue, which they are blaming on piracy. They are suing to recoup that loss. This makes sense, from their perspective.
On the other hand, the movie industry's profits have never been better. It's hard to claim piracy is having an impact if their profits are increasing.
While this is true, it is not good. I don't wish for this type of misfortune on my worst enemies, as if found legal, will still be a precedent for evil. Just like violence begetting violence, an eye for an eye makes the whole world blind. (Ghandi was a smart man)
YEah, when an image is simply a 1 x 1 picture that notifies the server, it lets the spammers know the mail is valid. No to mention all the stupid javascript exploits there could be. My question is: if you only read the text, is the rest of the stuff loaded behind the scenes? Should you even open these emails?
I've set my mail display to always be text based. It's a lot easier to detect spam that way too as most of the onscreen stuff is usually garbage, or funnily "get a real mail client".
Oh, and also, always use labeled line numbers in multipes of 10. That way, if you need to insert lines later in the middle, you have some line numbers to use later.
Use the minimum number of keywords in the language as possible. For example, all loops (for, while, do) can all be handled by a simple if and goto statement.
Since the internet has become 'privatized' it seems that there is not only cooperation between governments, but corporations as well. It seems that corporations have no consideration of freedoms and will sell out to the highest bidder. Witness the Great Firewall of China and the localized search features. It is scary because such governmental and corporate partnership indicates a possible rise of Global Fascism.
make me glad we still have Public Television. Sure, we have things like the Discovery Channel, but even that suite of networks has been taken over by ratings. I've noticed that the most recent documentaries are somewhat shallow, and sound bite driven. The Learning Channel used to be great, seems like all they have on now are wedding planner shows and interior decorating. What does that have to do with learning? I'm not claiming PBS is the greatest channel in the world, but at least they still value education.
JFK was assassinated Nov. 22, 1963. There was little more than 1 year (1 year and two or three months) left in the 1960-1964 term. If LBJ had been re-elected in 1968 he would have served no more than 9 years, 3 months, not 11 years.
I concurred. And then I jokingly asked if the study was sponsored by a brewery.
But that's no joke.
"The research was funded by Labatt and Guinness," said Trevithick, adding each brewery paid about $25,000 to finance the study. "But it's an unconditional grant and we made it very clear to them that if we had any findings we viewed as being appropriate to publish, that we'd publish them whether or not they were harmful to Labatt or Guinness."
It seems that overclocking the chips are all the rage these days, but I was excellent at Wolfenstein 3D when it first came out, because my computer ran at 20 Mhz and the minimum recommended speed was 25 Mhz. Slowing down the processor turns a real time game into a turn based game.
Now having said that, since overclocking requires massive cooling effects, would underclocking require that there be an external heat source? Or by underclocking, will an endothermic reaction occur, giving you a free air conditioner. Hmmm. I'll have to do some investigating here...
Slashdot Mirror
I'm going to try to give an example of Cantor's diagonalization method, to show that we can create a set which is "bigger" than the set of natural numbers.
Consider the set N, the set of natural numbers and the set X, where X is the set of all infinite binary sequences (i.e. all sequences {a(n),n=0..infinity|a(n) = 0 or 1}
Let's assume we can do a "1 to 1" correspondance between these two sets. If we can, we can find a function f(n) which when applied to the natural numbers will give f(1), f(2), f(3), and supposedly this will generate all members of X.
Let me create a new binary sequence that is not covered by that mapping.
Here is how I am going to create my sequence. For the first number in my sequence, I'm going to look at whatever f(1) is. Maybe it's {0,1,1,1,1,...} whatever. Whatever f(1) has as it's first number, I'm going to use the other number (0 if 1, 1 if 0), as the first number of my new sequence.
For the second number of my new sequence, I'm going to look at f(2), and the number in it's second position, and again, use the "other number".
For the third number in my sequence I'm going to use the "other" number than the third number in f(3), etc....
So for each position f(n), I will use the "other" number than the nth number in f(n).
What this gives me is a sequence that is guaranteed to be different than every f(n) sequence, because the number in position n is different.
Thus I have a new sequence. But this is supposedly impossible, because f(1), f(2), f(3) was supposed to be every sequence.
Thus, no function f exists. Thus this set X can not be put in a 1 to 1 correspondance with the natural numbers. Hope that helps.
has the current US Administration cared about treaties?
The obvious point to this message is to note that the RIAA and MPAA are in different situations. The music industry is seeing a SHARP DECLINE in revenue, which they are blaming on piracy. They are suing to recoup that loss. This makes sense, from their perspective.
On the other hand, the movie industry's profits have never been better. It's hard to claim piracy is having an impact if their profits are increasing.
That is the point of the quote.
While this is true, it is not good. I don't wish for this type of misfortune on my worst enemies, as if found legal, will still be a precedent for evil. Just like violence begetting violence, an eye for an eye makes the whole world blind. (Ghandi was a smart man)
YEah, when an image is simply a 1 x 1 picture that notifies the server, it lets the spammers know the mail is valid. No to mention all the stupid javascript exploits there could be. My question is: if you only read the text, is the rest of the stuff loaded behind the scenes? Should you even open these emails?
I've set my mail display to always be text based. It's a lot easier to detect spam that way too as most of the onscreen stuff is usually garbage, or funnily "get a real mail client".
Pedobytes? What?!!! I'm shocked.
ROUGE RUBICS CUBE!
Moulin Rogue would have been a more interesting movie...
Oh, and also, always use labeled line numbers in multipes of 10. That way, if you need to insert lines later in the middle, you have some line numbers to use later.
Use the minimum number of keywords in the language as possible. For example, all loops (for, while, do) can all be handled by a simple if and goto statement.
Hackers are Anti-Sheep , while others are content to keep thier heads down grazing on what is fed to them
So this is why hackers shun social contact? They would disappear in a bright flash of light if exposed to sheep?
What is a multi core processor?
This is the same public that watches Survivor? Reality TV gets all the ratings? Heck, even Sci Fi gets cancelled. I doubt they care.
Since the internet has become 'privatized' it seems that there is not only cooperation between governments, but corporations as well. It seems that corporations have no consideration of freedoms and will sell out to the highest bidder. Witness the Great Firewall of China and the localized search features. It is scary because such governmental and corporate partnership indicates a possible rise of Global Fascism.
If Cheney is Grand Moff Tarkin, and Bush is Darth Vader- who is Emperor Palpatine?
Karl Rove?
Yeah, that worked so well with the war on drugs. Oh , wait.
make me glad we still have Public Television. Sure, we have things like the Discovery Channel, but even that suite of networks has been taken over by ratings. I've noticed that the most recent documentaries are somewhat shallow, and sound bite driven. The Learning Channel used to be great, seems like all they have on now are wedding planner shows and interior decorating. What does that have to do with learning? I'm not claiming PBS is the greatest channel in the world, but at least they still value education.
Ironically, no he isn't. This is the one example of operator overloading Java allows.
(int) + (String) results in String.valueOf(int).concat(String)
JFK was assassinated Nov. 22, 1963. There was little more than 1 year (1 year and two or three months) left in the 1960-1964 term. If LBJ had been re-elected in 1968 he would have served no more than 9 years, 3 months, not 11 years.
It was set in the future (2000), and the headline in the paper said
Television replaced by Smellevision.
I expect similar results.
Answer: from the article
I concurred. And then I jokingly asked if the study was sponsored by a brewery.
But that's no joke.
"The research was funded by Labatt and Guinness," said Trevithick, adding each brewery paid about $25,000 to finance the study. "But it's an unconditional grant and we made it very clear to them that if we had any findings we viewed as being appropriate to publish, that we'd publish them whether or not they were harmful to Labatt or Guinness."
All orbit is is free fall with enough horizontal velocity to match. Orbit simply is fast free fall. Zero-g exists in orbit. How is this different?
What if songs on the radio get recorded? Will they want their cut? I know, fair use in all. See you in court.
Forgot to mention it was the Mac version.
It seems that overclocking the chips are all the rage these days, but I was excellent at Wolfenstein 3D when it first came out, because my computer ran at 20 Mhz and the minimum recommended speed was 25 Mhz. Slowing down the processor turns a real time game into a turn based game.
Now having said that, since overclocking requires massive cooling effects, would underclocking require that there be an external heat source? Or by underclocking, will an endothermic reaction occur, giving you a free air conditioner. Hmmm. I'll have to do some investigating here...