Code signing is more a convenience (or inconvenience) than any kind of guarantee or real restriction. Modern computers are serious von Neumann machines -- it's difficult to distinguish data and code.
It's not that simple. Heat engines all need a strong heat gradient to operate: both a source and a good sink. With no atmosphere to conduct heat, building a heat sink is surprisingly difficult. Radiating out into space (which, at a few Kelvin, is pretty cold) just isn't all that efficient once you're talking about objects that are producing substantial amounts of heat.
Just so you know, a tax rebate is simply when tax paid is greater than tax owed. Most tax filers who get rebates are getting back some fraction of the money that they already paid through withholding.
The income at which a family can manage to pay zero tax (that is, their rebate is equal in size to the total withheld) is roughly the same as the median income (which in turn is about twice the poverty level). About 36% of income tax filers paid zero or less tax, although of course there are many cases where you are not required to file income tax forms at all.
Where "usually" in this case apparently means "if you have a Linux computer rather than a Windows or Macintosh computer or a DVD player". Which means not usually.
Of course, while you may also be breaking the law when you simply decrypt the DVD with something like dvdcss, you certainly don't need file sharing to do that. Playing on unsupported platforms and format shifting isn't really relevant to the issue of downloading the movie, as you can do all of that just fine with the DVD.
You couldn't. Photons don't work like distinct particles, really. If you want a light signal that's localized in space, it will consist of multiple photons and will spread out as it travels. The EM wave packet will interfere with nearby wave packets in much the same way as you describe.
Then you're being deceptive. The wording of your original post clearly suggests that the toxicity of CO2 is somehow relevant. For human pollution and the atmosphere, it's not.
More or less. At least, where I went to school, there's 3 exams: Q exam, which qualifies you for the doctorate program, A exam, which makes you a real doctoral candidate, and B exam, your thesis defense. Passing the A exam grants you an MS, if you check the appropriate boxes on forms.
It's substantially more complicated than that. Any system for producing and consuming electricity dumps heat into the environment at a lot of stages (well, every stage, really). The waste heat produced by solar panels is roughly the same as the waste heat produced by generating electricity using fossil fuels. But that quantity of waste heat pales in comparison to the quantity of heat retained as a result of the CO2 added to the atmosphere by burning the fossil fuels.
So, to a reasonable degree of accuracy, solar panels (and waste heat in general) don't contribute to global warming and burning fossil fuels does.
CO2 is toxic at about 100 times the current concentration in the atmosphere. I don't think we could reach that atmospheric concentration if we burnt up every bit of fossil fuel on the planet.
Maybe if you watched more Mythbusters, you'd recognize that your "method" bears no resemblance to science. (Okay, fine, it also bears no resemblance to a study of constitutional law.)
I temporarily got you confused with the idiots. My mistake.
I can't think offhand of somewhere in mathematics that floor is used outside of computing and other finite-precision applications. The general problem is that decimal representations of numbers are not unique. So, a method of applying the floor function that naively relies on the decimal representation is incorrect. Since 0.999... is strictly an alternate representation for the number one, floor(0.999...) = floor(1) = 1. But, as you joke, no simple, obvious-to-humans ways of evaluating floor based on the decimal representation (a fancy way of saying "drop everything to the right of the decimal") is actually correct.
To, er, further add to this, the original statement of 1+2+3+4+...=-1/12 is at least a thing. It's the Ramanujan sum. That's not really the same as a proper sum, though, and is far afield from "0.999... = 1".
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second one orders a half a beer. The third orders a quarter of a beer. The bartender says, "You're all idiots," and pours two beers.
They're not proving "0.99999 = 1" at all. That's not true. They're proving that "0.999... = 1". One is an infinite sequence of digits, and the other isn't. The distinction is important. The proof of "0.999... = 1" has nothing to do with rounding, and to suggest so indicates a (common) gross misunderstanding of the problem.
First, you only measure things with such poor precision because you're working well above the quantum level.
Second, natural numbers are certainly important. For one, they're critical to our understanding of the rest of mathematics, which is important for fancy things like being able to take measurements and manipulate them at all. For another, we work with whole numbers of objects all the time -- two apples, ten antelope, four huts, etc. It's not "10 +/- 0.01 antelope".
This is the mistake everyone makes. The "..." signifies an infinite sequence. There's not any digit at the end. It's not meaningful to put "..." in the middle of a decimal number and then have digits after it. (This is different from the meaning of "..." in text, which is often used to signify that some finite amount of text has been elided.)
Only in a few cases (and the notable case of "infinity is not a number"). Anyone familiar with the derivation of limits, derivatives, and integrals should be familiar with finite numbers that are the result of an infinite-step process.
No, only if you have a finite number of 9s. The "..." indicates an infinite sequence of "9" digits, which is exactly 1 (which rounds, uninterestingly, to 1).
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Code signing is more a convenience (or inconvenience) than any kind of guarantee or real restriction. Modern computers are serious von Neumann machines -- it's difficult to distinguish data and code.
Magnetic fields do no work.
It's not that simple. Heat engines all need a strong heat gradient to operate: both a source and a good sink. With no atmosphere to conduct heat, building a heat sink is surprisingly difficult. Radiating out into space (which, at a few Kelvin, is pretty cold) just isn't all that efficient once you're talking about objects that are producing substantial amounts of heat.
Just so you know, a tax rebate is simply when tax paid is greater than tax owed. Most tax filers who get rebates are getting back some fraction of the money that they already paid through withholding.
The income at which a family can manage to pay zero tax (that is, their rebate is equal in size to the total withheld) is roughly the same as the median income (which in turn is about twice the poverty level). About 36% of income tax filers paid zero or less tax, although of course there are many cases where you are not required to file income tax forms at all.
Where "usually" in this case apparently means "if you have a Linux computer rather than a Windows or Macintosh computer or a DVD player". Which means not usually.
Of course, while you may also be breaking the law when you simply decrypt the DVD with something like dvdcss, you certainly don't need file sharing to do that. Playing on unsupported platforms and format shifting isn't really relevant to the issue of downloading the movie, as you can do all of that just fine with the DVD.
You couldn't. Photons don't work like distinct particles, really. If you want a light signal that's localized in space, it will consist of multiple photons and will spread out as it travels. The EM wave packet will interfere with nearby wave packets in much the same way as you describe.
Denature, actually. Nothing kills enzymes, as they're not alive.
Then you're being deceptive. The wording of your original post clearly suggests that the toxicity of CO2 is somehow relevant. For human pollution and the atmosphere, it's not.
More or less. At least, where I went to school, there's 3 exams: Q exam, which qualifies you for the doctorate program, A exam, which makes you a real doctoral candidate, and B exam, your thesis defense. Passing the A exam grants you an MS, if you check the appropriate boxes on forms.
It's substantially more complicated than that. Any system for producing and consuming electricity dumps heat into the environment at a lot of stages (well, every stage, really). The waste heat produced by solar panels is roughly the same as the waste heat produced by generating electricity using fossil fuels. But that quantity of waste heat pales in comparison to the quantity of heat retained as a result of the CO2 added to the atmosphere by burning the fossil fuels.
So, to a reasonable degree of accuracy, solar panels (and waste heat in general) don't contribute to global warming and burning fossil fuels does.
CO2 is toxic at about 100 times the current concentration in the atmosphere. I don't think we could reach that atmospheric concentration if we burnt up every bit of fossil fuel on the planet.
Maybe if you watched more Mythbusters, you'd recognize that your "method" bears no resemblance to science. (Okay, fine, it also bears no resemblance to a study of constitutional law.)
I temporarily got you confused with the idiots. My mistake.
I can't think offhand of somewhere in mathematics that floor is used outside of computing and other finite-precision applications. The general problem is that decimal representations of numbers are not unique. So, a method of applying the floor function that naively relies on the decimal representation is incorrect. Since 0.999... is strictly an alternate representation for the number one, floor(0.999...) = floor(1) = 1. But, as you joke, no simple, obvious-to-humans ways of evaluating floor based on the decimal representation (a fancy way of saying "drop everything to the right of the decimal") is actually correct.
Which is probably why it so disturbs people!
Mathematicians are distinctly countable.
Wrong. 0.999... is exactly 1.
Any finite number of "9" digits is less than 1. An infinite sequence of "9" digits is exactly 1.
To, er, further add to this, the original statement of 1+2+3+4+...=-1/12 is at least a thing. It's the Ramanujan sum. That's not really the same as a proper sum, though, and is far afield from "0.999... = 1".
Sorry, I mean that 1-2+3-4 is still divergent. It's something, but I no longer remember the appropriate math terminology. :-)
You've got it very wrong.
1+2+3+4+... is a divergent series.
1-2+3-4+..., on the other hand, is a convergent series. It turns out it converges on 1/4. Which is still disturbing.
That is, the sum over all positive N of N * (-1)^(N+1) = 1/4.
I prefer the integral. That way, you can build one out of electrical components.
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second one orders a half a beer. The third orders a quarter of a beer. The bartender says, "You're all idiots," and pours two beers.
This isn't insightful, it's wrong. Painfully, painfully wrong.
They're not proving "0.99999 = 1" at all. That's not true. They're proving that "0.999... = 1". One is an infinite sequence of digits, and the other isn't. The distinction is important. The proof of "0.999... = 1" has nothing to do with rounding, and to suggest so indicates a (common) gross misunderstanding of the problem.
First, you only measure things with such poor precision because you're working well above the quantum level.
Second, natural numbers are certainly important. For one, they're critical to our understanding of the rest of mathematics, which is important for fancy things like being able to take measurements and manipulate them at all. For another, we work with whole numbers of objects all the time -- two apples, ten antelope, four huts, etc. It's not "10 +/- 0.01 antelope".
8.99999..991
This is the mistake everyone makes. The "..." signifies an infinite sequence. There's not any digit at the end. It's not meaningful to put "..." in the middle of a decimal number and then have digits after it. (This is different from the meaning of "..." in text, which is often used to signify that some finite amount of text has been elided.)
Only in a few cases (and the notable case of "infinity is not a number"). Anyone familiar with the derivation of limits, derivatives, and integrals should be familiar with finite numbers that are the result of an infinite-step process.
No, only if you have a finite number of 9s. The "..." indicates an infinite sequence of "9" digits, which is exactly 1 (which rounds, uninterestingly, to 1).