And then, there are those of us who know the laws, don't have to be reminded of them, and break them anyway. The fallen world is the one with so many damned laws that a person cannot make it through a single day without breaking at least one of them. Seatbelt laws indeed --- my life, my decision.
He's got a valid point. It is not sufficient to complete an ordered field via Cauchy sequences to get a structure isomorphic to the reals. In addition, the field must have the Archimedean property that for every x,y in the field, there exists a natural number n such that nx>y. This plus Cauchy complete is equivalent to Dedekind complete (least upper bound property). It is the Dedekind complete ordered fields that are isomorphic to the reals.
I'm not following you. Could you be more specific with the ordering of the rational functions? For example, using the notation (3,2,1) for 3+2x+x^2, how does (5,0,-7)/(4,2,13) compare to (-8,3)/(5,11,-2,9) ?
Furthermore, what is an open interval for these functions? Are you talking about epsilon neighborhoods with respect to some metric?
Completeness in the real numbers is not that every Cauchy sequence converges, it is that every set bounded above has an upper bound.
That should be "has a LEAST upper bound."
That real Cauchy sequences converge follows from this property, but not the other way around.
False. One way to construct the reals is to consider equivalence classes of Cauchy sequences of rationals. The reals constructed in this manner have the least upper bound property.
For an example take rational functions as your field with an order on their coefficients(ie 1x+1 > 1x > 1 > 1/x). Showing that cauchy sequences converge and that this not equivalent to the reader is left as an exercise to the reader.
What topology are you considering on this space of functions?
It's not linear --- the breaking distance is proportional to the square of the velocity.
Assuming constant acceleration a applied by the breaks, the change in kinetic energy of the vehicle (m/2) v^2 equals the work done on the vehicle W=mas where s is the stopping distance. Therefore, s=(1/2a) v^2.
Yeah. I guess all ASCII text files are effectively compressed too. I mean, they don't use all 8 bits of a byte, now do they? Wow! Look at all the hard drive space that observation freed up!!! Idiot.
Hey cockbag, you might want to review your dictionary as well. You don't know what effectively means. It means, in an effective manner. So, to be applicable here, there would have to be a real reduction in the amount of space used to store the data. There isn't. You're wrong. Go blow yourself.
It sounds like you don't know jack shit about theory. Whether 100 consecutive samples have the value 0 or 32000 has nothing to do with file compression. Go back to school troll.
I agree with several other respondents. I'm a cinephile who enjoys viewing foreign, independent, and lesser known films (in addition to the occasional Hollywood blockbuster). Netflix has a fantastic selection, and I average about $1.50/disc, which beats anything the local competition has to offer.
how employable do you think someone is going to be if they go into the workforce having never used windows?
I don't know. One of my friends from high school ended up as head of R&D at Hitachi Data Systems. You know what he learned about computers in high school? BASIC on a CBM 8032.
I agree, we are the government. The problem is that money is god. If I want to run for office (and have a chance of winning) I need lots of money. If a corporation or small group of billionaires wants something, all they have to do is pump enough money into the legislative slot machine until JACKPOT! If I want something, I have to start a grassroots movement across the nation and convince millions of voters that not only do they want what I want, but that they should write their congress-critters and vote accordingly. Not exactly a level playing field, is it?
Not to attack what you said in any way, but FOIL has always been a pet peeve of mine. It doesn't extend to multiplying a pair of trinomials for instance. I wish the textbooks would get away from that type of silliness and call it what it is: another application of the distributive property, with which the student should already be familiar.
I was about to be clever and say "Just pull a Lou Reed on 'em", but after searching for some amusing links I discovered that labels apparently have a MMM clause in the artists' contracts to prevent exactly that. Oh well.
I don't go to Ebay to save $1 on something I can buy at Target or Amazon. I go there to buy things that aren't for sale locally or online. There's no other realistic choice if I want those things.
How difficult can it be? There are several ripping applications (some of them free of charge) that effortlessly back up the DVD and strip out all CSS, copy protection, UOPs, etc.
Slashdot Mirror
The kids are in school to learn
No, they are in school to have their wills broken and to be indoctrinated.
like Français, Deutsch, or Español?
The lesson is not to stop "wrong" behavior. The lesson is not to get caught.
Or, I use a much easier resource (the Internet) for my research.
That's fine if you only mind scraping the surface of knowledge.
I buy books instead of borrowing them.
That's fine too, for those of us fortunate to have several thousand dollars to throw down for book purchases.
For those looking for old, rare, out-of-print volumes or for journal articles, the library is just about the only resource.
And then, there are those of us who know the laws, don't have to be reminded of them, and break them anyway. The fallen world is the one with so many damned laws that a person cannot make it through a single day without breaking at least one of them. Seatbelt laws indeed --- my life, my decision.
He's got a valid point. It is not sufficient to complete an ordered field via Cauchy sequences to get a structure isomorphic to the reals. In addition, the field must have the Archimedean property that for every x,y in the field, there exists a natural number n such that nx>y. This plus Cauchy complete is equivalent to Dedekind complete (least upper bound property). It is the Dedekind complete ordered fields that are isomorphic to the reals.
I'm not following you. Could you be more specific with the ordering of the rational functions? For example, using the notation (3,2,1) for 3+2x+x^2, how does (5,0,-7)/(4,2,13) compare to (-8,3)/(5,11,-2,9) ?
Furthermore, what is an open interval for these functions? Are you talking about epsilon neighborhoods with respect to some metric?
Completeness in the real numbers is not that every Cauchy sequence converges, it is that every set bounded above has an upper bound.
That should be "has a LEAST upper bound."
That real Cauchy sequences converge follows from this property, but not the other way around.
False. One way to construct the reals is to consider equivalence classes of Cauchy sequences of rationals. The reals constructed in this manner have the least upper bound property.
For an example take rational functions as your field with an order on their coefficients(ie 1x+1 > 1x > 1 > 1/x). Showing that cauchy sequences converge and that this not equivalent to the reader is left as an exercise to the reader.
What topology are you considering on this space of functions?
It's not linear --- the breaking distance is proportional to the square of the velocity.
Assuming constant acceleration a applied by the breaks, the change in kinetic energy of the vehicle (m/2) v^2 equals the work done on the vehicle W=mas where s is the stopping distance. Therefore, s=(1/2a) v^2.
The Bible and the Koran are MORE dangerous than smoking.
No matter how many times you repeat it, the data is not compressed --- practically, effectively, or otherwise.
There is no effect on the recipient, other than receiving a signal substantially different from what the artist intended.
Now, get sucking, bitch. I like slow, then fast.
You'll have to tell your father to quit flossing his teeth with that microscopic filament you call a penis before anyone else can get a crack at it.
Yeah. I guess all ASCII text files are effectively compressed too. I mean, they don't use all 8 bits of a byte, now do they? Wow! Look at all the hard drive space that observation freed up!!! Idiot.
Hey cockbag, you might want to review your dictionary as well. You don't know what effectively means. It means, in an effective manner. So, to be applicable here, there would have to be a real reduction in the amount of space used to store the data. There isn't. You're wrong. Go blow yourself.
So does the data use less space on the disc or not? If not, it ain't compressed. Period. End of story.
It sounds like you don't know jack shit about theory. Whether 100 consecutive samples have the value 0 or 32000 has nothing to do with file compression. Go back to school troll.
Dynamic range compression and file size compression are two different things.
I agree with several other respondents. I'm a cinephile who enjoys viewing foreign, independent, and lesser known films (in addition to the occasional Hollywood blockbuster). Netflix has a fantastic selection, and I average about $1.50/disc, which beats anything the local competition has to offer.
how employable do you think someone is going to be if they go into the workforce having never used windows?
I don't know. One of my friends from high school ended up as head of R&D at Hitachi Data Systems. You know what he learned about computers in high school? BASIC on a CBM 8032.
Wow. I mean like, how is that possible?
I agree, we are the government. The problem is that money is god. If I want to run for office (and have a chance of winning) I need lots of money. If a corporation or small group of billionaires wants something, all they have to do is pump enough money into the legislative slot machine until JACKPOT! If I want something, I have to start a grassroots movement across the nation and convince millions of voters that not only do they want what I want, but that they should write their congress-critters and vote accordingly. Not exactly a level playing field, is it?
Not to attack what you said in any way, but FOIL has always been a pet peeve of mine. It doesn't extend to multiplying a pair of trinomials for instance. I wish the textbooks would get away from that type of silliness and call it what it is: another application of the distributive property, with which the student should already be familiar.
I was about to be clever and say "Just pull a Lou Reed on 'em", but after searching for some amusing links I discovered that labels apparently have a MMM clause in the artists' contracts to prevent exactly that. Oh well.
I don't go to Ebay to save $1 on something I can buy at Target or Amazon. I go there to buy things that aren't for sale locally or online. There's no other realistic choice if I want those things.
This law may make no sense, but if you want it changed, you have to contect your elected representatives and bribe them to change it.
There. Fixed that for you.
How difficult can it be? There are several ripping applications (some of them free of charge) that effortlessly back up the DVD and strip out all CSS, copy protection, UOPs, etc.