Recent content by grmnsplx

What he said.

Who is trying to modify set theory? My understanding was that Cantor's set theory was proven to be inconsistent (by Russel and Zermelo and perhaps others) so a more axiomatic approach was necessary. The issue is this: a set is defined by it's elements. So I can come up with all sorts...

Such paradoxes exist because we are able to construct sentences to which there may or may not be any grounds in reality. We can ask all sorts of silly questions as well. "What colour is Wednesday?" for example. In the case of the barber paradox, though, the assumptions lead to a...

Yes, that's right. If I am not mistaken, it looks like I am doing a Least ordinary squares.

*bump*

p→q is read "p implies q" or "if p then q" That is, by definition, if p is true then so is q. So if p were true, and q were not true then, p→q would not be a true statement. Does that make sense? We can go through a proof if you like.

Hello all. I am not a stats person so I would like some help/confirmation on this one. What I am trying to achieve (if possible) is a metric on how two portfolios (or strategies) are correlated. Imagine there are two portfolios of assets A,B,C,D... with different weights of each asset...

as robert said, the grad student may have been talking about some non-Eulidean geometry. If we take away one of Euclid's axioms, we make all new geometries and some of our inferences such as the law of sines may disappear. Anyway, ask him about it again and put it on the forum.

you have the right answer. you disproved the statement by giving a counter example. "eg x=-2 y= -1 then this statement will not hold but how should i put in down" first assume that the statement is true if x < y for all x,y implies that x^2 < y^2, then we have that (-2 < -1 implies...

I doubt this will have a pretty substitution Maybe use the generalized binomial expansion... If that works you'll probably get a hypergeometric solution.

You don't like the idea of "expanding space"? What exactly do you take issue with?

yeah be careful with the infinite series. 0=+1 + (-1) right? so 0= 1-1+1-1+1-1+1-1... = 1+(-1+1)+(-1+1)+(-1+1)... = 1 +0+0+0+0... =1 which is a load of crap

one more key point for mathematics. the limit solves a huge problem in mathematics and that is dividing by zero. Mathematicians avoid dividing by zero like the plague. By taking the limit, we really don't have to worry so much about dividing by zero.

Good question. I'd say Calculus is a very useful branch of mathematics which lends itself very well to real physical problems. Common problems we can solve using calculus might be falling objects or the orbit of planets and moons, where our variables are time, velocity, distance, acceleration...

montoyas7940 said it: quotient rule. Unless you are specifically asked to use the definition of the derivative, but I can't imagine why?