If you really wanted a meritocracy, you'd have to separate children from their parents at birth--parents wouldn't know their children and children wouldn't know their parents. That way, every child would start out with a similar environment and none would get the benefits of wealth or the...
Do you mean per practitioner or as a whole? We as a society probably spend more on teachers than celebrities, but the former group greatly outnumbers the latter, so each A-list celebrity gets a bigger piece of the pie. Compare how many students a teacher can effectively teach with how many...
Obviously the attorney's statement will be phrased in such a way that it doesn't imply any wrongdoing on the part of his client. The cop writing a police report is also unlikely to include anything that could later be used to incriminate him. Cops can get in trouble for lying in a police report...
I'm surprised the town council managed to stay composed throughout that whole speech. I know people have the right to speak at public meetings without being cut off and told they're not making any sense, but I'll bet they desperately wanted to make an exception this one time. As Churchill said...
If we go down to the atomic level, the human body doesn't really have an inside. Anything sufficiently small can pass between the atomic nuclei. We are over 99.9% empty space after all.
If \frac{S_{n}}{s} < 1
then \frac{s}{S_{n}} > 1
since Sn > 0 for sufficiently large n. In that case,
|log(\frac{S_{n}}{s})| = -log(\frac{S_{n}}{s}) = log(\frac{s}{S_{n}}) \leq \frac{s }{S_{n}} - 1
So, we can say that
|log(S_{n}) - log(s)| \leq max\left\{\frac {S_{n}}{s} - 1, \frac...
Lord Jim by Joseph Conrad is an excellent book.
I would also recommend Machiavelli, both The Prince and Discourses on Livy. The difference between the two was surprising, to say the least.
Let's see...
log(S_{n}) - log(s) = log(\frac{S_{n}}{s}) \leq \frac{S_{n}}{s} - 1
And
\frac{S_{n}}{s} - 1 = \frac{S_{n} - s}{s}
Clearly, the right side goes to 0 as n goes to infinity. I'll skip the formal arguments, but it should work if s>0. Guess we didn't need continuity after...
If that was the case, they wouldn't be independent. If you want an example, take two quarters, give one to a friend, and start flipping them. Define a random variable for you and your friend (say, Y and F). Their distribution will be the same, but they're unlikely to be equal.
That logic is flawed. Try it out with some numbers:
1<2 and 2<4, but 1-2 > 2-4
You need the continuity of the logarithm to ensure that log(Sn) and log(s) are close as n increases without bound.
Supporting 50 billion people would be difficult, but might not be impossible. I think there's enough space to pull it off. Loads of people would have to live in the desert, on ships, or even underground in order to clear up enough arable land to support the amount of farming needed to feed...
Perhaps. Still, many countries really don't want to see China any more powerful than it absolutely needs to be. Directly to the south, by Malaysia and Indonesia, is a major shipping route carrying oil from the Middle East to Japan and the United States. If China ends up dominating Southeast...
The world is far too interdependent for a massive regional conflict not to have global repercussions. The first step would obviously be to try and broker a peace settlement, but if that fails the rest of Southeast Asia as well as Pakistan would quickly join the fray. Countries like Japan or the...
Most politicians don't have the knowledge necessary to understand the complexity of today's financial markets. One practically needs a Ph. D for that. Even if they could, little things like poverty, healthcare, crime, national defense, and upcoming elections also require their time. That's where...