Actually, if (P) is "for every a, b, a+b = b+a", then (!P) is "there exists a, b such that a+b != b+a". All it takes to contradict (P) is to find one pair... Zero, obviously, does not satisfy this with any a or b, so one would be left to find something else that works to disprove (P).
If memory serves, the group of integers is, by definition, defined by the generator "given n in the group, there exists m such that m = n+1. Group implies, by definition, closure, associativity, identity and invertability.
Your follow-up discussion is, if memory serves, very much the demonstration that the addition of two natural numbers is commutative. The same for their inverts follows from the group's invertability:
m + n = n + m
Adding (-n) + (-m) from the right, and (-m) + (-n) from the left:
Not quite. I forgot to write down "for any a" and later in particular zero.
My math classes are a distant souvenir, but I do recollect having seen a demonstration that the group of integers as defined by the group integers, whose generator is n(k + 1) = n(k) was necessarily commutative...
Some googling yields that any cyclic group is necessarily abelian:
Pardon for correcting, but some Americans aren't sold on the theory. In less religious countries, aka everywhere bar the most completely backwards areas on the planet, there is no debate whatsoever.
If they're planning to pay their workers as little as possible (market wages), then it doesn't matter so much where they set up their business.
You'd rather the job be created elsewhere while you're left paying for unemployment benefits? (Or prison warden salaries, if the unemployeds' lack of welfare is such that they turn to crime to eat?)
Get over it. The 90k/year immigrant is quick to note that he can make a better wage elsewhere, and the company will be looking for a new guy as soon as he moves on. Plus, the odds are they're only offering you the interview because the spotted the immigrant, and they need to show immigration officials that they failed to locate the needed candidate before sponsoring a visa. The real issue here isn't the immigrant, it's the immigration policy, the hiring policy and the going bout of deflation.
... because that's how it currently feels when you want to get a US visa with a strong education and the intention to create a company there. Scratch that; this doesn't even remotely begin to describe US immigration officials. I'd wager that they export more US jobs (by having them created elsewhere, directly or indirectly) than all other professions combined.
Seriously... Just open the floodgates and let anyone who applies with a degree come and settle, including those after lower quintile jobs. People with education are more likely to create a business, and those that don't increase the supply of trained staff. Cost-free, at that. The "they'll steal low-wage jobs" point is hogwash. Nobody wants the lowest paid jobs anyway, the newcomers would do away with the housing inventory in a snap, and China would have an extremely hard time making its factories work if their production engineers all migrated to the US. (Remember that NYT story about how Apple decided to produce the iPhone in China because, amongst other things, fielding a few thousands of production engineers could be done in China in a matter of weeks instead of months?)
Also, consider the drive, the resourcefulness and the taste for risk-taking that are needed to successfully cross the Rio Grande or the Mediterranean Sea. In either case, you need to not take no for an answer when you applied the legal way, save hard-earned cash to pay whoever is taking you on the other side, and there is a non-negligible likelihood that you'll get robbed, murdered or (if a woman) forced into sex slavery. If those skills don't fit the successful entrepreneur, I don't know what does. And if crime gets less cash because the flood gates are open, all the better.
Lastly, it is surprising that livestock and poultry can cross borders freely, but actual people cannot. We may have gotten our priorities wrong when passports were introduced in the 19th century. Then again, if the plebeians cannot escape to better places, wages are kept in check.
Blaming tests doesn't solve any problems. Why don't we have kids build rockets AND take tests?
How about fixing the tests before doing both?
My recollection of the US education system (I was in primary school) includes silly multiple choice tests done with a pencil. Looking back, and presuming things haven't changed much since there was an article recently on a school board member who couldn't complete a 10th grader's math test, I'd suggest it's lunacy.
I looked into a 10th grade test around when that article was on Slashdot, and did it in very much the same way as I did tests when I was in primary school: I'd look at the answers and then, barely reading the question, I'd eliminate those that were clearly wrong based on the figures that popped out while scanning the question. That's a very screwed up way to test math imho. My parents clearly recall me reaching out for the optimal solution: focusing on how to do the test instead of on understanding what the test was supposed to be testing. (Luckily, I was curious enough to do both, but I certainly surprised them enough that they rehash the story 30-years later.)
In France, here's how you test(ed?) math and physics (and much about everything else, in fact): you ask a series of questions. And then the kid, on a separate piece of paper, needs to provide an argumented answer. Both words count. Half of the grade goes for providing the correct answer. The other half goes to the underlying reasoning and argumentation, which you need to put down on paper as well. A similar process applied in Germany when I attended school there. The main difference was that you had a formula booklet and a calculator -- you were expected to know your formulas and how to do complicated calculations by hand in France.
The process reaches its climax if you head towards Sup/Spé (these are two years after high school if you want to attend our Ivy League schools). The Math-II test leading to Normal Sup, which trains researchers, is (or was when I passed it, anyway) a yet to be resolved mathematical problem. Correcters get no material since the solution to the problem fed to the students is simply unknown. What they're tasked to grade are your insights and the quality of your reasoning. (And yes, a few of them are actually solved by students in the allocated time. My math teacher then, had picked up a habit of inserting a bonus question to keep the brightest in the weekly exam room for more than two hours. His despair was unequivocal when his PhD got solved in the remaining two.)
I'm glad they lost, but when I think patent trolling, I usually think of a bogus shell company that hasn't actually created anything. They're just paper companies dumping cash into legal action to turn a profit, designed to shield the players behind it from any kind of retribution.
Doesn't that description fit Oracle nicely, when it comes to their suit vs Google? Not saying Google did anything right, but, best I'm aware, Oracle primarily purchased Sun for the potential to sue over Java-related patents. Their attorneys were reportedly drooling all over the patent portfolio.
move slowly and oppress/order citizens in a very hierarchical manner, because that's how large kingdoms survive for many centuries.
Citation?
I fail to see why a large kingdom or nation would necessarily need to be oppressive. The largest of all kingdoms, in history, was late 19th century England. It survived centuries. It arguably had to deal with the occasional mob at home or in its colonies. It did so in much the same as France or the US at the time. Crowd control techniques, back then, would consist in lining the army in front of it, and shooting at the crowd when it got too close -- much like they did in Jackson State or Tiananmen.
By the way, great valley civilizations (Nile, Mesopotamia, Indus, Gange, China) were indeed very centralized and less individualistic, but this likely had a lot to do with agriculture: small groups of farmers could deforest any area and grow crop throughout Europe, whereas large scale infrastructure was needed to take advantage of floods or monsoon in the great valleys. Large scale coordination and entrenched mutual assistance was needed to survive, in the latter case.
CoffeeScript... That way, when your console tells you you've a JS error on line X, you need to check the code output by CS, and locate whatever code you wrote that could have generated the relevant lines, all the while coping with the fact that CS doesn't cover 100% of JS, and introduces its own set of bugs and quirks on top of those in JS. Good luck with that in the long term.
Depending your project's specifics, consider whether you actually need the web application. If it turns out that you don't, go straight for an Android app (since you know Java). After it's released, toss in a "dumb" (aka no admin area) web site -- it should amount to a couple of new (outsourced) views for whichever framework you picked to create your json or XML API.
I suggest this because writing complicated/interactive web views is a true mess for the uninitiated. The devil is in the plethora of browser-specific quirks, and you probably want to avoid running into them if you can get away with it.
If you really must, that said, there are lots of MVC frameworks for web development, including several in Java. Each language has its more popular ones; picking yours is, imho, mostly a matter of taste...
You aren't going to get a space ride unless you are insanely rich or an astronaut willing to devote decades to a career in hopes of getting a shot, so stop dreaming.
There used to be a time when the same held for air flights.
There reportedly are over a million kids who are home schooled in the US. And a whole bunch of sites that cater to parents who give it a shot.
Not all of these parents are good at math, physics, and so on. Maybe she could locate enough of them in your area to make a living, or work for (or create) a site in that field.
Slashdot Mirror
Per TFA, the fetus' DNA is in its mom's blood. So you cannot get any (non-random) information prior to conception.
Actually, if (P) is "for every a, b, a+b = b+a", then (!P) is "there exists a, b such that a+b != b+a". All it takes to contradict (P) is to find one pair... Zero, obviously, does not satisfy this with any a or b, so one would be left to find something else that works to disprove (P).
If memory serves, the group of integers is, by definition, defined by the generator "given n in the group, there exists m such that m = n+1. Group implies, by definition, closure, associativity, identity and invertability.
Your follow-up discussion is, if memory serves, very much the demonstration that the addition of two natural numbers is commutative. The same for their inverts follows from the group's invertability:
m + n = n + m
Adding (-n) + (-m) from the right, and (-m) + (-n) from the left:
(-m) + (-n) = (-n) + (-m)
Not quite. I forgot to write down "for any a" and later in particular zero.
My math classes are a distant souvenir, but I do recollect having seen a demonstration that the group of integers as defined by the group integers, whose generator is n(k + 1) = n(k) was necessarily commutative...
Some googling yields that any cyclic group is necessarily abelian:
http://en.wikipedia.org/wiki/Cyclic_group
BSD is dying trolls are dying too.
Suppose there exists b for which a + b != b + a.
Therefor 0 + b != b + 0, and thus b != b.
Absurd, thus the hypothesis is false.
QED.
Per other comment in the tread:
http://www.redorbit.com/news/science/1112388659/nobel-prize-winner-leaves-group-over-global-warming/
Doesn't about half of the US population give credence to creationism?
http://en.wikipedia.org/wiki/Level_of_support_for_evolution#Public_support
Pardon for correcting, but some Americans aren't sold on the theory. In less religious countries, aka everywhere bar the most completely backwards areas on the planet, there is no debate whatsoever.
Whether it succeeds or fails in Europe isn't relevant. The real deal is China and whether anything they pass there is actually enforced.
But they sure as hell take note when a majority of the relevant committees recommend against.
If they're planning to pay their workers as little as possible (market wages), then it doesn't matter so much where they set up their business.
You'd rather the job be created elsewhere while you're left paying for unemployment benefits? (Or prison warden salaries, if the unemployeds' lack of welfare is such that they turn to crime to eat?)
Even from a company like Ireland or Canada, there are quotas.
Ireland and Canada are companies?
Get over it. The 90k/year immigrant is quick to note that he can make a better wage elsewhere, and the company will be looking for a new guy as soon as he moves on. Plus, the odds are they're only offering you the interview because the spotted the immigrant, and they need to show immigration officials that they failed to locate the needed candidate before sponsoring a visa. The real issue here isn't the immigrant, it's the immigration policy, the hiring policy and the going bout of deflation.
... because that's how it currently feels when you want to get a US visa with a strong education and the intention to create a company there. Scratch that; this doesn't even remotely begin to describe US immigration officials. I'd wager that they export more US jobs (by having them created elsewhere, directly or indirectly) than all other professions combined.
Seriously... Just open the floodgates and let anyone who applies with a degree come and settle, including those after lower quintile jobs. People with education are more likely to create a business, and those that don't increase the supply of trained staff. Cost-free, at that. The "they'll steal low-wage jobs" point is hogwash. Nobody wants the lowest paid jobs anyway, the newcomers would do away with the housing inventory in a snap, and China would have an extremely hard time making its factories work if their production engineers all migrated to the US. (Remember that NYT story about how Apple decided to produce the iPhone in China because, amongst other things, fielding a few thousands of production engineers could be done in China in a matter of weeks instead of months?)
Also, consider the drive, the resourcefulness and the taste for risk-taking that are needed to successfully cross the Rio Grande or the Mediterranean Sea. In either case, you need to not take no for an answer when you applied the legal way, save hard-earned cash to pay whoever is taking you on the other side, and there is a non-negligible likelihood that you'll get robbed, murdered or (if a woman) forced into sex slavery. If those skills don't fit the successful entrepreneur, I don't know what does. And if crime gets less cash because the flood gates are open, all the better.
Lastly, it is surprising that livestock and poultry can cross borders freely, but actual people cannot. We may have gotten our priorities wrong when passports were introduced in the 19th century. Then again, if the plebeians cannot escape to better places, wages are kept in check.
You can't reduce education to numbers. (...)
Blaming tests doesn't solve any problems. Why don't we have kids build rockets AND take tests?
How about fixing the tests before doing both?
My recollection of the US education system (I was in primary school) includes silly multiple choice tests done with a pencil. Looking back, and presuming things haven't changed much since there was an article recently on a school board member who couldn't complete a 10th grader's math test, I'd suggest it's lunacy.
I looked into a 10th grade test around when that article was on Slashdot, and did it in very much the same way as I did tests when I was in primary school: I'd look at the answers and then, barely reading the question, I'd eliminate those that were clearly wrong based on the figures that popped out while scanning the question. That's a very screwed up way to test math imho. My parents clearly recall me reaching out for the optimal solution: focusing on how to do the test instead of on understanding what the test was supposed to be testing. (Luckily, I was curious enough to do both, but I certainly surprised them enough that they rehash the story 30-years later.)
In France, here's how you test(ed?) math and physics (and much about everything else, in fact): you ask a series of questions. And then the kid, on a separate piece of paper, needs to provide an argumented answer. Both words count. Half of the grade goes for providing the correct answer. The other half goes to the underlying reasoning and argumentation, which you need to put down on paper as well. A similar process applied in Germany when I attended school there. The main difference was that you had a formula booklet and a calculator -- you were expected to know your formulas and how to do complicated calculations by hand in France.
The process reaches its climax if you head towards Sup/Spé (these are two years after high school if you want to attend our Ivy League schools). The Math-II test leading to Normal Sup, which trains researchers, is (or was when I passed it, anyway) a yet to be resolved mathematical problem. Correcters get no material since the solution to the problem fed to the students is simply unknown. What they're tasked to grade are your insights and the quality of your reasoning. (And yes, a few of them are actually solved by students in the allocated time. My math teacher then, had picked up a habit of inserting a bonus question to keep the brightest in the weekly exam room for more than two hours. His despair was unequivocal when his PhD got solved in the remaining two.)
Look at the bright side: creationists would have it their way in their communities.
You Sir, should watch 5 dangerous things kids should do:
http://www.ted.com/talks/gever_tulley_on_5_dangerous_things_for_kids.html
I'm glad they lost, but when I think patent trolling, I usually think of a bogus shell company that hasn't actually created anything. They're just paper companies dumping cash into legal action to turn a profit, designed to shield the players behind it from any kind of retribution.
Doesn't that description fit Oracle nicely, when it comes to their suit vs Google? Not saying Google did anything right, but, best I'm aware, Oracle primarily purchased Sun for the potential to sue over Java-related patents. Their attorneys were reportedly drooling all over the patent portfolio.
move slowly and oppress/order citizens in a very hierarchical manner, because that's how large kingdoms survive for many centuries.
Citation?
I fail to see why a large kingdom or nation would necessarily need to be oppressive. The largest of all kingdoms, in history, was late 19th century England. It survived centuries. It arguably had to deal with the occasional mob at home or in its colonies. It did so in much the same as France or the US at the time. Crowd control techniques, back then, would consist in lining the army in front of it, and shooting at the crowd when it got too close -- much like they did in Jackson State or Tiananmen.
By the way, great valley civilizations (Nile, Mesopotamia, Indus, Gange, China) were indeed very centralized and less individualistic, but this likely had a lot to do with agriculture: small groups of farmers could deforest any area and grow crop throughout Europe, whereas large scale infrastructure was needed to take advantage of floods or monsoon in the great valleys. Large scale coordination and entrenched mutual assistance was needed to survive, in the latter case.
the average person doesn't give a rats ass about privacy
... until you show her Girls Around Me or some similarly intrusive or creepy app.
CoffeeScript... That way, when your console tells you you've a JS error on line X, you need to check the code output by CS, and locate whatever code you wrote that could have generated the relevant lines, all the while coping with the fact that CS doesn't cover 100% of JS, and introduces its own set of bugs and quirks on top of those in JS. Good luck with that in the long term.
Yeah, you can do a lot of weird things, too.
$a = array('7.1'); // true
var_dump(in_array('7.10', $a));
http://www.phpwtf.org/
Depending your project's specifics, consider whether you actually need the web application. If it turns out that you don't, go straight for an Android app (since you know Java). After it's released, toss in a "dumb" (aka no admin area) web site -- it should amount to a couple of new (outsourced) views for whichever framework you picked to create your json or XML API.
I suggest this because writing complicated/interactive web views is a true mess for the uninitiated. The devil is in the plethora of browser-specific quirks, and you probably want to avoid running into them if you can get away with it.
If you really must, that said, there are lots of MVC frameworks for web development, including several in Java. Each language has its more popular ones; picking yours is, imho, mostly a matter of taste...
http://en.wikipedia.org/wiki/Comparison_of_web_application_frameworks
For javascript, don't miss jQuery and qUnit.
You aren't going to get a space ride unless you are insanely rich or an astronaut willing to devote decades to a career in hopes of getting a shot, so stop dreaming.
There used to be a time when the same held for air flights.
There reportedly are over a million kids who are home schooled in the US. And a whole bunch of sites that cater to parents who give it a shot.
Not all of these parents are good at math, physics, and so on. Maybe she could locate enough of them in your area to make a living, or work for (or create) a site in that field.