Just a note—sin^2(x) cannot be sin(sin(x)) because that is a datatype error.
You just showed that you don't know enough mathematics.
The input to the sine function is not an angle, it is a real or complex number. If real, this number often (but not always!) describes some angle. If complex, it obviously won't describe an angle.
The sine function is defined as
sin x = (exp(i x) - exp(-i x)) / (2i)
where i is the imaginary number, and exp(x) is defined by the series
exp x = 1 + x + x^2/2 +... + x^n/n! +...
Note that, since the convergence radius of the exponential series is infinite, and the sine is just a linear combination of exponentials, the sine is defined on all complex numbers. Since it is complex-valued, sin sin x is indeed well defined for all complex numbers x.
Moreover, if you restrict the sine to real numbers (that is, only accept real numbers), you still have a well defined sin sin x, because the real sine function is also real-valued (more exactly, its values are restricted to the interval [-1,1]).
Also, the output is in general not a rational number (the only thing you could have meant with "ratio" that makes sense in this context).
Sure, you can use workarounds like MathJAX. But it doesn't mean it is more than a workaround. What happens if you want to read some HTML containing formulas while offline?
A math tag would have allowed me to type math in my response to you right here
HTML also supports Γ but you'll not get Slashdot to display it. What makes you think that a math tag would be supported, if it doesn't even support all characters usually found in formulas?
MathML is supported in IE natively (at least it is for IE 10). What makes you say otherwise? Just head on over to http://www.mathjax.org/demos/mathml-samples/ and see for yourself.
I don't have IE10 and therefore cannot tell whether it does or does not support MathML, however I just want to make sure you've seen that this page by default does not render MathML, but builds the formulas with HTML+CSS. You have to explicitly select "MathML" with the dropdown selector to see what it looks like rendered using MathML.
MathML is a static content description language like (pure) HTML, not a programming language like JavaScript. Moreover, it should use the same parser used for all other XML based content (like XHTML), which is most likely even the same parser which is used to parse HTML. So I cannot see how MathML could be used for an exploit which is not possible for HTML (unless you did a really crappy implementation).
It's only theft if it not part of the contract. Just as it is not theft if the cashier demands that you give him money for the goods you got from the store.
You don't pay in bitcoins. You pay the electricity bill for mining the bitcoins. If the bitcoin value goes down, your electricity bill still stays high.
This is RMS. For RMS, everything which is not (uppercase) Free Software is bad. This includes (non-Free) samples, demos or rentals with a limited lifespan.
You can certainly pronounce AM as a word. People don't usually do that, but it's definitely possible. On the other hand, SCSI can't really be pronounced as a word. However people do anyway, by inserting an "A" where there's none, i.e. pronouncing it as if it were written "SCASI".
Or in short: The difference between initialism and acronym isn't as clear-cur as it seems.
Who cares what tools it was built with? If I build an operating system with MSVC++, do I have to prefix "Microsoft/"? I rather assume I'd get sues by MS for trademark infringement if I did so.:-)
It would certainly be cheaper for me to pay you the money you'd be making from that mining than paying my electricity provider more than you make from that mining. I don't feel like subsidizing my electricity provider.
All that's of course assuming your program is worth the cost to me.
Yeah, that's the problem with you Americans. Your don't acknowledge that all important Slashdot stories occur on May 1, and thus you need to get a free day at that day. All other countries have a free day today.
By burning fossil fuels we're essentially reversing that process. It's worth noting that those biological processes are still ongoing and to some extent auto-compensating.
But we are actively working on stopping that compensation by destroying the rainforest, which is not only one of the most important CO2 sinks, but also one of the most important O2 sources.
They don't. If they did, creation of a particle-antiparticle pair would cost no energy. It is experimentally verified that it costs energy. More exactly, it costs twice the rest energy of the particle, which experimentally proves that the energy of the antiparticle is the same as the energy of the particle.
Also from the theoretical foundations they have positive energy. You may be confused by the fact that the antiparticle corresponds to the negative-energy solutions in the Dirac equation. However, those negative solutions in the Dirac equation also have the same, not the opposite charge.
What happens is easiest understood in the Dirac see model. Here it is assumed that the negative energy states are all filled in vacuum. Then a particle-antiparticle pair created by exciting a negative energy particle into positive energy, leaving a "hole" in the negative energy states. Such a hole acts exactly like a particle (called antiparticle) with all properties of the particle that would be in that state reversed. So now what is the energy of the antiparticle? Well, it is the negative of the energy a particle would have if it filled the hole. But the energy of such a particle would be negative because, after all, it's a negative energy state. Now the negative of a negative energy is a positive energy.
I should warn that the Dirac see model is not the modern viewpoint (for example, it doesn't work for bosons), however the properties of the antiparticles are not changed by newer theories.
Mathematics is different from philosophy. Philosophers try to say something about the real world, albeit with different methods than natural sciences. Mathematicians on the other hand don't try to say anything about the real world. They analyse the structure of mathematical/logical constructs, no matter where those constructs come from (most early constructs came from natural sciences, but there are now also many constructs which cannot be found in nature; try to find the smallest uncountable ordinal number in our world!).
Slashdot Mirror
You just showed that you don't know enough mathematics.
The input to the sine function is not an angle, it is a real or complex number. If real, this number often (but not always!) describes some angle. If complex, it obviously won't describe an angle.
The sine function is defined as
sin x = (exp(i x) - exp(-i x)) / (2i)
where i is the imaginary number, and exp(x) is defined by the series
exp x = 1 + x + x^2/2 + ... + x^n/n! + ...
Note that, since the convergence radius of the exponential series is infinite, and the sine is just a linear combination of exponentials, the sine is defined on all complex numbers. Since it is complex-valued, sin sin x is indeed well defined for all complex numbers x.
Moreover, if you restrict the sine to real numbers (that is, only accept real numbers), you still have a well defined sin sin x, because the real sine function is also real-valued (more exactly, its values are restricted to the interval [-1,1]).
Also, the output is in general not a rational number (the only thing you could have meant with "ratio" that makes sense in this context).
Sure, you can use workarounds like MathJAX. But it doesn't mean it is more than a workaround. What happens if you want to read some HTML containing formulas while offline?
HTML also supports Γ but you'll not get Slashdot to display it. What makes you think that a math tag would be supported, if it doesn't even support all characters usually found in formulas?
MathML is supported in IE natively (at least it is for IE 10). What makes you say otherwise? Just head on over to http://www.mathjax.org/demos/mathml-samples/ and see for yourself.
I don't have IE10 and therefore cannot tell whether it does or does not support MathML, however I just want to make sure you've seen that this page by default does not render MathML, but builds the formulas with HTML+CSS. You have to explicitly select "MathML" with the dropdown selector to see what it looks like rendered using MathML.
MathML is a static content description language like (pure) HTML, not a programming language like JavaScript. Moreover, it should use the same parser used for all other XML based content (like XHTML), which is most likely even the same parser which is used to parse HTML. So I cannot see how MathML could be used for an exploit which is not possible for HTML (unless you did a really crappy implementation).
In other words, it's an evolution of strategies.
They didn't have acronyms back in the 19th century, silly.
I always thought that acronyms were invented by IBM.
They used so many of them that the same 3 letters often applied to 5 different products. At the same time.
See? They already had quantum computing!
I just got the RAM filling up and the computer going to a crawl until I forcefully killed firefox.
The computer is performing a musical?
It's only theft if it not part of the contract. Just as it is not theft if the cashier demands that you give him money for the goods you got from the store.
You don't pay in bitcoins. You pay the electricity bill for mining the bitcoins. If the bitcoin value goes down, your electricity bill still stays high.
I was already running Warp 3 in 1995! :-)
(OS/2 Warp 3, to be exact)
I prefer the content to be played. :-)
This is RMS. For RMS, everything which is not (uppercase) Free Software is bad. This includes (non-Free) samples, demos or rentals with a limited lifespan.
You can certainly pronounce AM as a word. People don't usually do that, but it's definitely possible. On the other hand, SCSI can't really be pronounced as a word. However people do anyway, by inserting an "A" where there's none, i.e. pronouncing it as if it were written "SCASI".
Or in short: The difference between initialism and acronym isn't as clear-cur as it seems.
Who cares what tools it was built with? If I build an operating system with MSVC++, do I have to prefix "Microsoft/"? I rather assume I'd get sues by MS for trademark infringement if I did so. :-)
It would certainly be cheaper for me to pay you the money you'd be making from that mining than paying my electricity provider more than you make from that mining. I don't feel like subsidizing my electricity provider.
All that's of course assuming your program is worth the cost to me.
I'm sure you got downmodded because you forgot the "???" step. ;-)
I'd guess it's the density of the substrate electrons, disturbed by the atoms.
Yeah, that's the problem with you Americans. Your don't acknowledge that all important Slashdot stories occur on May 1, and thus you need to get a free day at that day. All other countries have a free day today.
Slashdot should add "P.S.=>" to the lameness filter.........
Or simply too much boldface.
But we are actively working on stopping that compensation by destroying the rainforest, which is not only one of the most important CO2 sinks, but also one of the most important O2 sources.
They don't. If they did, creation of a particle-antiparticle pair would cost no energy. It is experimentally verified that it costs energy. More exactly, it costs twice the rest energy of the particle, which experimentally proves that the energy of the antiparticle is the same as the energy of the particle.
Also from the theoretical foundations they have positive energy. You may be confused by the fact that the antiparticle corresponds to the negative-energy solutions in the Dirac equation. However, those negative solutions in the Dirac equation also have the same, not the opposite charge.
What happens is easiest understood in the Dirac see model. Here it is assumed that the negative energy states are all filled in vacuum. Then a particle-antiparticle pair created by exciting a negative energy particle into positive energy, leaving a "hole" in the negative energy states. Such a hole acts exactly like a particle (called antiparticle) with all properties of the particle that would be in that state reversed. So now what is the energy of the antiparticle? Well, it is the negative of the energy a particle would have if it filled the hole. But the energy of such a particle would be negative because, after all, it's a negative energy state. Now the negative of a negative energy is a positive energy.
I should warn that the Dirac see model is not the modern viewpoint (for example, it doesn't work for bosons), however the properties of the antiparticles are not changed by newer theories.
Newtonian Physics had also been confirmed to many digits in many experiments. And then came Relativity and Quantum Mechanics.
Yes, nobody expects antimatter to fall up. But then, nobody expected the Michelson-Morley experiment to give a null result either.
Mathematics is different from philosophy. Philosophers try to say something about the real world, albeit with different methods than natural sciences. Mathematicians on the other hand don't try to say anything about the real world. They analyse the structure of mathematical/logical constructs, no matter where those constructs come from (most early constructs came from natural sciences, but there are now also many constructs which cannot be found in nature; try to find the smallest uncountable ordinal number in our world!).