Recent content by Ryuzaki

What kind of an assumption do I need? Could you give an example? Also, if P = (0,0,0), how do you get the expected coordinates of the object to be (0,0,0)? Doesn't it depend on the values of the probabilities of the object being within each shell?

Suppose there's an object within a sphere of radius 5-metres from a given point P=(x_0,y_0,z_0). The probabilities of the object being within 0-1, 1-2, 2-3, 3-4 and 4-5 metres of P are given to be respectively p_1,p_2,p_3,p_4 and p_5. With this information, is it possible to find the expected...

I’m working on a chemistry problem, which essentially translates to finding the answer to a related probability problem. However, my knowledge in probability is very limited and I'd be grateful if someone could help me out with it. The following is the problem:- Suppose I have a bag containing...

In a paper that I'm reading, the authors write:- N_e \approx \frac{3}{4} (e^{-y}+y)-1.04 ------------ (4.31) Now, an analytic approximation can be obtained by using the expansion with respect to the inverse number of "e-foldings" (N_e is the number of "e-foldings"). For instance, eq...

Right you are. Found this out the hard way. :biggrin: Quite embarrassing, but I actually do. :redface: It's where I try to knock some math sense to my non-math friends.

I guess I was being naive. Hardly anyone uses FB for discussing math. Just thought it'd be cool though.

I know this isn't the appropriate place to post this, but I just couldn't stop myself after hearing something this big (to me atleast!)! I urge you to read through the following carefully:- There is currently an online petition at Change.org for the implementation of LaTeX in Facebook! For...

Since A \approx B, there exists a one-to-correspondence from A to B, and thus, it must have an inverse, which is another one-to-one correspondence from B to A. So, the symmetric property is satisfied. I'm not sure about proving the transitive property. If a f is a one-to-one correspondence...

Sorry if I sounded assertive. I don't have a teacher. I'm self-learning from a text named A Concrete Introduction to Higher Algebra, by Lindsay N. Childs. Ah, sorry about that. Guess it doesn't make much sense when I read it now. An identity mapping should do the trick, shouldn't it?

Why is it that I can't use it? I thought it would be generalized if I prove it this way, using the number of elements. But then, doesn't the demonstration of such a function depend on A, or to be precise, the domain of A? How can this work for any general A?

Come to think of it, I do not know what set of axioms the text assumes. It hasn't mentioned anything so far about it (I'm still in the first chapter!). The text is A Concrete Introduction to Higher Algebra, by Lindsay N. Childs. This question isn't part of the text exercise, but I thought of...

Homework Statement Prove that the relation, two finite sets are equivalent if there is a one-to-one correspondence between them, is an equivalence relation on the collection S of all finite sets. I'm sure I know the gist of how to do it, but I'm a beginner in proofs, and I'm not sure if...

Oh, I think I understand yours and Office_Shredder's posts now. I came up with a proof, and I'd be grateful if you could check if its correct. Proof that the class S of all non-empty finite sets is infinite. Assume that S is finite. Now, for every set T \in S, there exists a set {T} \in...

I'm sorry, but I'm not able to understand this (probably because of the Latex malfunction). But in the text I'm using, 0 is not constructed along with the natural numbers. So, there is no S_0. EDIT: Truly sorry, I guess I should have mentioned this in the beginning. I just re-read the text and...

Sorry if this sounds stupid (I'm a beginner in the subject), but don't you have to prove that your collection of sets goes on till infinity? I mean, intuitively, I can see that it goes on, but how do you prove it? In other words, how do you show that your collection of sets is "obvious"?