Recent content by rustynail

I mean ''equivalent under the relation of equality'' as in ''A and B are the same object''. Because A and B share not only the same cardinality, but also the same elements. So if A = {p, q, r, t}, then B = {p, q, r, t} also, and thus A=B. Edit : I'm currently looking at the Zermelo-Fraenkel...

Doesn't that only say that all elements of A are also elements of B, making A a subset of B, and not necessarily equivalent to B? Or does using ''iff'' imply that ## x \in B ## iff ## x \in A ## ? Also, I understand that the way I put it isn't the most direct way of doing it, but I want to know...

I am starting to learn propositional calculus and am trying to make sense of the notation. I am trying to express the idea that sets A and B are equivalent. I want to know if the following statement is true and if it shows three equally valid ways of saying that A and B are the same set...

Look up for ''Metric'' on wikipedia. Also, note that while a manifold does have a local metric, it does not necessarily have a ''global'' metric defining distances between any two points.

Great, I appreciate, thank you!

Hello, I was playing around with DeMoivre's formula ei*pi = -1 and there is something I don't quite understand about taking the natural logarithm of a certain expression. I though that e2i*pi = 1 ln[e2i*pi] = ln (1), but this yields to an imposibility 2i*pi = 0. So...

Complex numbers, much like vectors, are quantities defined by both a modulus (norm) AND an argument (direction). An infinity of complex numbers share the same norm, but have different arguments. The other way around is also true. Therefore, |z| = |w| does not imply z = w.

thanks AGNuke, you mean that some approximations could get me closer to an integer coefficient? Do you think my attempt at a solution made sense?

Hello, I am currently taking a college level chemistry class. I am struggling with this problem, any help would be greatly appreciated. Homework Statement We have a certain quantity of CuSO_{4} \cdot \gamma H_{2}O If our sample is formed of (25,5% Cu), (12% S), (57,7% O) and (4.04% H)...

I just want to clarify things. What you want is problems in which we have found errors, and you want us to show you the problems for you to find these errors? I don't think this would yield a lot of results for you to work on. Or do you want us to give you just ANY problem and see if you can...

Thank you DH for the help, and DonAntonio for your rigor, I need to work on that. But in this part, \sum_{r=0}^{\infty} \frac{(-1)^r(s\ln n)^r}{r!} Don't we need to to take the sum of all terms with both n and r, from 1 to ∞? Could I write it as \sum_{n=1}^{\infty} \; \sum_{r=0}^{\infty}...

I was playing a bit with the Riemann Zeta function, and have been struggling with some notation problems. The function is defined as follows \zeta (s) = \sum_{n=1}^{\infty} \frac{1}{n^s} where s \in \mathbb{C} we know that n^s = exp(s\;ln\;n) so I can write \zeta (s) =...

you got [2^(k+1)](2k). multiply 2^(k+1) by two, that is raising your exponent by 1. Hence 2^(k+2)

Thank you robphy! Very interesting indeed.

Hello forum! I would like to begin by stating that I am no expert in general relativity, nor in physics or mathematics, although I have some basic understanding of calculus and linear algebra. So if you can keep the math simple, I would appreciate. Also, please correct me if I'm wrong. As...