Recent content by Charles007

We say two permutations f and g commute if fg = gf. Same as A group G said to be commutative, or ablian if operation *, in addition to be above four axioms, satisfies. Commutativity, For all x,y belongs to G, we have x*y = y*x ==================================== Can we use this...

We say two permutations f and g commute if fg = gf. I only know. Permutation (abc)(defgh) have order 15. (123)(45678) have order 15. I don't know the permutation (123)(45678) in s8 or not. how to verify it? =================================== (123)(456) is a permutation has order 3...

Hello, can anyone tell me how to find order 15 in S8. I only know. Permutation (abc)(defgh) have order 15. Next, I would think about 8*7*6*5*4*3*2*1 = 13440 Number of permutations, for order 15 in s8. would be 8*7*6*5*4*3*2*1 / 3*5 = 896. There are 896 permutation of order 15 in...

Hello, can anyone tell me how to find order 15 in S8. I only know. Permutation (abc)(defgh) have order 15. Next, I would think about 8*7*6*5*4*3*2*1 = 13440 Number of permutations, for order 15 in s8. would be 8*7*6*5*4*3*2*1 / 3*5 = 896. There are 896 permutation of order 15...

OK. thx. :smile:

Just remember it? right?

I know how to find the adjugate of 3x3 matrix. from the defination. How to find adjugate of 2x2 matrix. e.g A= ( 1 3 ) ______( 2 4 ) adjoint . I know how to find adjugate and inverse. of 3 * 3 matrix First . I find matrix of cofactor. from the defination. (n-1)(n-1) matrix * (sign...

Thank you very much, :approve: I am understand now.

Let A and B be non-empty and bounded subsets of R. What it is mean by bounded?

Thank you very much. Now I know what I should do next. Collect all defination of group and connect them using your collection. One more question. suppose we have a set A (-12,3]. (-x)------(-12)---------0-------------3----------------------------x They minum for set A is -12, and...

so we know x > 0, x - x_0 > -\delta =〉 x_0 > delta or x_0 - delta > 0 U said IT doesn't work. what is IT.? where can I put it in and verify it?

Since x_0 is positive, we might as well ensure that x is positive by letting \delta \leq \frac{x_0}{2} (note we could choose \frac{x_0}{4} or something similar, but half of x_0 is convenient). Hence x > \frac{x_0}{2}, and we have a bound for the term \frac{1}{x^2} since \frac{1}{x^2} <...

I still don't understand how to get it. :frown:

One more question. How, the supremum, the least upper bound. Infimum, , supremum. what is it mean? Attempt. for example, 1,. (0,15] 2, {n/2n+1|n belongs to nautral number (N)}

THese days. I am trying to tidy up with my summary notes. I got surjective homomophism, isomorphic, and cyclic group, Subgroup, normal group, symmetric group, Quaternion group, and quotient group. How to distinguish them. Is there any tric to understand and remember these. I am...