You can find a proof of this here for example. The idea is to use Euler's product formula for the zeta-function and the well-known fact that the harmonic series diverges.
Interestingly enough, it is known that the sum of the reciprocals of twin primes converges (and the sum is approximately 1.90216054). Of course, if there is only finitely many twin primes, this statement is trivial.
Eh? The p-adic numbers form a field (well, one field for every p), so in particular they are an abelian group under addition, which means that additive inverses (and subtraction) exist.
MathML was never really intended for writing by hand, and even if Apropos makes it easier, I can't see myself switching from (La-)TeX anytime soon. I can enter extremely complex mathematical expressions at least 20-30 times faster by typing them in TeX than I ever could do clicking around an interface like Apropos.
MathML is a good idea in theory, but until there are good tools for writing and editing MathML, there will be very few people using it (either for publishing or for archival purposes.)
According to the best estimates there are about 10^81 elementary particles in the universe.
There is a nice qoute by Eddington saying: I believe there are 15 747 724 136 275 002 577 605 653 961 181 555 468 044 717 914 527 116 709 366 231 425 076 185 631 031 296 protons in the universe and the same number of electrons. Nothing wrong with his self-confidence;)
Geostationary orbit is about 36,000 km (not 36,000 m...), and as you said cruising altitude is about 1 km, so I would imagine that the difference in latency is hardly worth mentioning.
Hafnium may be a component of zirconium ore, but the isomer Hf-178m does not exist naturally (even though standard Hf-178 constitutes about 28% of the Hf on earth).
One review of Wolfram's book which I found most interesting and entertaining is written by Stephen Krantz (professor of Mathematics at Washington U, St. Louis) and is available here
Ahhh, the story behind the Fahrenheit scale is kind of funny. Fahrenheit's idea was to let 100 degrees be normal body temperature, and 0 degrees to be the coldest temperature he coud achieve (with a ice/salt mixture). Unfortunately, things didn't go quite as he planned... For the 0 degree baseline, he used a ice/salt mixture that was not the best one known at the time -- he should have been able to get the temperature down another notch or two. As for 100 degrees being normal body temperature -- well, his test tubes were not perfect: small bumps on the inside of the tube caused the scale to be slightly off.
There will always be idiots around, the "human factor" can't be removed completely. Nevertheless there is a big difference between having a bunch of idiots running a nuclear power plant and say a hydroelectric power plant in terms of what will happen when things go wrong.
Well actually, the usual view of science is that should be refutable, not that it is or should be provable. Religion on the other hand is notoriously non-refutable.
Sorry to have to point out that there was no such thing as set theory at the time of Plato and Aristotle. (And neither of them made any significant contribution to the field of mathematics either...)
Insightful? You mean that the only patters are periodic? Of course, pi is irrational and hence has a non-periodic expansion in any base. But there are certainly other patterns in the world than periodic ones, since pi can be described using a finite amount of information, of course there are patterns to pi as to any other computable number.
Slashdot Mirror
Interestingly enough, it is known that the sum of the reciprocals of twin primes converges (and the sum is approximately 1.90216054). Of course, if there is only finitely many twin primes, this statement is trivial.
+4 Informative???? That page contains no information whatsoever. Plenty of nonsense though.
Eh? The p-adic numbers form a field (well, one field for every p), so in particular they are an abelian group under addition, which means that additive inverses (and subtraction) exist.
MathML is a good idea in theory, but until there are good tools for writing and editing MathML, there will be very few people using it (either for publishing or for archival purposes.)
Eh? Reboot to change resolution or font DPI? At the very worst you'd have to restart the X server.
Hmmmm, a death rate of 0.05% per year... does that mean that dutch injecting drug users have a life expectancy of 2000 years?
Well, (La-)TeX is Turing complete, I would definitely call it a programming language.
According to the best estimates there are about 10^81 elementary particles in the universe.
;)
There is a nice qoute by Eddington saying: I believe there are 15 747 724 136 275 002 577 605 653 961 181 555 468 044 717 914 527 116 709 366 231 425 076 185 631 031 296 protons in the universe and the same number of electrons. Nothing wrong with his self-confidence
Geostationary orbit is about 36,000 km (not 36,000 m...), and as you said cruising altitude is about 1 km, so I would imagine that the difference in latency is hardly worth mentioning.
Albert's not-so-well-known brother?
Hafnium may be a component of zirconium ore, but the isomer Hf-178m does not exist naturally (even though standard Hf-178 constitutes about 28% of the Hf on earth).
Just as long as nobody mentions the third sets of secrets, everything should be fine.
Just remember, I_M_God2U could be the one who is thinking about hiring you ;)
One review of Wolfram's book which I found most interesting and entertaining is written by Stephen Krantz (professor of Mathematics at Washington U, St. Louis) and is available here
Ahhh, the story behind the Fahrenheit scale is kind of funny. Fahrenheit's idea was to let 100 degrees be normal body temperature, and 0 degrees to be the coldest temperature he coud achieve (with a ice/salt mixture). Unfortunately, things didn't go quite as he planned... For the 0 degree baseline, he used a ice/salt mixture that was not the best one known at the time -- he should have been able to get the temperature down another notch or two. As for 100 degrees being normal body temperature -- well, his test tubes were not perfect: small bumps on the inside of the tube caused the scale to be slightly off.
There will always be idiots around, the "human factor" can't be removed completely. Nevertheless there is a big difference between having a bunch of idiots running a nuclear power plant and say a hydroelectric power plant in terms of what will happen when things go wrong.
Hmm, 500,000 out of 700,000 would be about 71% of the market...
Well actually, the usual view of science is that should be refutable, not that it is or should be provable. Religion on the other hand is notoriously non-refutable.
Of course, a horsepower is not a measure of energy but of power. Hence the name... :)
i'd say quartic
Sorry to have to point out that there was no such thing as set theory at the time of Plato and Aristotle. (And neither of them made any significant contribution to the field of mathematics either...)
Is there really anyone who thinks Echelon is ok??
Insightful? You mean that the only patters are periodic? Of course, pi is irrational and hence has a non-periodic expansion in any base. But there are certainly other patterns in the world than periodic ones, since pi can be described using a finite amount of information, of course there are patterns to pi as to any other computable number.
Why isn't the followup named "The Tensor"?