Recent content by DEMJ

Also, I still do not understand how to list all the elements because this is the only element I know how to find. Should I do (234165)^3, (234165)^4, ... on up to what exponent?

Ok so I could write an element as (234165)^2 as \left(\begin{array}{llllll} 1 & 2 & 3 & 4 & 5 & 6\\ 2 & 3 & 4 & 1 & 6 & 5\\ \end{array}\right) \circ \left(\begin{array}{llllll} 1 & 2 & 3 & 4 & 5 & 6\\ 2 & 3 & 4 & 1 & 6 & 5\\ \end{array}\right) = (3412)(56)

So that is one element, right? But how do I go about finding the rest. And more important, how could I know exactly how many elements there will be?

I don't understand because on the wiki page above it says that (1 2 3 4 5 6)^2 = (1 3 5)(2 4 6) but when I compose (123456) with (123456) = (123456). I guess I am just royally confused.

What do you mean take the powers of the element? Could you give me an example of one? Thank you so much.

Homework Statement List the elements of the cyclic subgroup of S_6 generated by f = \left(\begin{array}{llllll} 1 & 2 & 3 & 4 & 5 & 6\\ 2 & 3 & 4 & 1 & 6 & 5\\ \end{array}\right)Homework Equations The Attempt at a Solution I really do not understand what the elements of a permutation really...

You are right, I owned my self by basic algebra :-p

that would make a_k b_k = \frac{(-1)^{2k}}{k} which is convergent, I think. I meant what I put but apparently it does not work?

Homework Statement If a_k is decreasing and it's limit is 0 as k \to \infty and \sum_{k+1}^{\infty} b_k converges conditionally, then \sum_{k=1}^{\infty} a_k b_k converges Homework Equations This is true or false. The Attempt at a Solution I think it is false because if we let...

Homework Statement If \sum_{k=1}^{\infty} a_k converges and a_k/b_k \to 0 as k\to \infty, then \sum_{k=1}^{\infty} b_k converges.Homework Equations It is true or false.The Attempt at a Solution I think it is false and here is my counterexample. Let a_k = 0,b_k=\frac{1}{k}. This satisfies our...

I just made a thread here https://www.physicsforums.com/showthread.php?t=399124 and now whenever I try to use latex to create a new thread I get the same latex stuff from this thread I linked. Here for example lol a^2 \sup hi how are you and what I typed for each one is [.tex]lol[/tex]...

Homework Statement if a_k \le b_k for all k \in \mathbb{N} and \sum_{k=1}^{\infty} b_k is absolutely convergent, then \sum_{k=1}^{\infty} a_k converges. Homework Equations It's either true or false. The Attempt at a Solution I think a counterexample to prove it's false is if we...

Homework Statement Use Euler's formula to write 2^{1-i} in the form a+ib. The Attempt at a Solution I know this has to be so simple because I could do this easy if the question was to write e^{1-i} in the form a+ib using Euler's. So what I do not understand is how does 1-i being...

I am doing awful with this, but I understand (47) sends 7 to 4, but I do not understand where (12) sends 7 -> 4 to? If it sends it (246) does it change (246) to (276) ?

If I start at the right 7 -> 4 then 4 goes back to 7. Then 2 -> 1 then 1 goes back to 2. or should I think of it as 7 -> 4 then 4 -> 2 then 2 -> 1 then 1 -> 6 and so on. Which is the correct way to think for permutation multiplication?