HalfWit

A friend of Sir Cumflex, who always wore a little pointed hat.

Brits treat plurals differently than Americans. For example a Brit will say, "The team are travelling to London," rather than the American "The team *is* travelling." Same with "maths." Due to an innovation in British English (BrE), collective nouns can take either singular (formal agreement) or plural (notional agreement) verb forms, according to whether the emphasis is on the body as a whole or on the individual members respectively; compare a committee was appointed with the committee were unable to agree.[11][12] The term the Government always takes a plural verb in British civil service convention, perhaps to emphasize the principle of cabinet collective responsibility. http://en.wikipedia.org/wiki/Comparison_of_American_and_British_English It's a good thing America won the revolutionary war, otherwise today we'd all be speaking English.

Solving a hard math problem is nothing like starting from axioms and blindly trying to reach the desired theorem. Look at Wiles's proof of FLT. He spent seven years attacking the problem with new ideas from the field of advanced algebraic number theory. The idea in math is to have an insight. Computers don't have insights; or at the very least, we have not yet figured out how to create a machine that has insights. We might do so in the future, but how would we even approach the problem? It's very difficult. Contrast math with chess; a discipline in which it was once thought that human players using insight could always defeat a "look-ahead" computer program. But it turns out that chess programs can use brute-force algorithms to defeat the best human players in the world. In the field of chess-related artificial intelligence, brute-force algorithms have handily won out over insight or gestalt algorithms. But math genuinely is different. Advanced math is about finding a new perspective, building a new conceptual structure, or even using new foundational principles. You can't just bang together axioms and hope a valuable theorem will drop out. Because the definition of "valuable" is a subjective, esthetic value judgment made by human mathematicians.

I'd say that's negative rep. "Number" obviously means "positive integer" in the context of the question. It's silly to say "OOh you forgot to say you're working in positive integers, gotcha gotcha."

Because 1/3 is the multiplicative inverse of 3 in the real numbers; and 6 * (1/3) = 2. The application to biological entities such as oranges is better left to advanced courses in applied mathematics. I think math pedagogy would be improved if we would refrain from confusing fractions with rational numbers.

No that is not true. The radius of the unit circle is 1. The angular measure of the circumference is 2pi radians. The circumference is 2pi but the angular measure is 2pi radians. In other words the length of the circumference is 2pi. The measure of the angle swept out by the radius moving around the circle is 2pi radians. It's the angle that's measured in radians.

The radius is 5000 meters. The circumference is 2i*r = 10,000 pi = 2pi radians; so 1 radian = 5000 meters. We are circling at 100 m/s so we'll travel 5000 meters = 1 radian in 50 seconds. If we travel 1 radian in 50 seconds then we'll go 1/50 = .02 radians in 1 second. So the answer is .02 radians per second. In general, here is how to stop your headaches and learn to know and love radians.. The unit circle has radius 2pi and everything flows from that. 1/4 of the way around the circle is pi/2; halfway round is pi; 3/4 of the way around is 3pi/2; all the way round is 2pi, which is the same as zero, where we started. Forget you ever heard of degrees. They're a fading memory from your past. From now on, think only in radians. When you get confused remember that the circumference of the unit circle is 2pi radians and all other circles are proportional to that. And if t is a fraction between zero and one, going t of the way around the circle is 2pi*t radians. If t = 1/2 then you went halfway around the circle, to pi. If t = 1/3 then you went 1/3 of the way around the circle to 2pi/3. After a while you won't even care about how many degrees that is. That's the mindset you want to strive for. Think only in radians from now on.

This is the same idea as a line segment of length 1 being made up of an infinity of points, each of which is of length zero. Calculus or not, it's really a philosophical mystery. I don't think anyone knows the answer. I would go so far as to say that calculus and even advanced mathematics doesn't address this question at all. There is no branch of mathematics that allows us to add up an uncountable infinity of points of length zero to get a line segment of length 1. There is no answer to this riddle as far as I know.

I've heard it said that if you divided all the money in the world equally among all the people in the world; within five years every dollar would be back in its original hands.

I've decoded this for you. It says: Leave the money under the old oak tree. Don't call the cops or else Fluffy gets it.