Click
ID:114614
 Jun 16 2011, 7:04 am
|
|
|
Jun 16 2011, 7:11 am
|
|
EmpirezTeam
 |
I've discovered an error in section 3.1 I believe where you declare that the properties were both associate and communiative, you might want to revise that as there is nothing that shows it's associate.
|
EmpirezTeam wrote:
you might want to revise that as there is nothing that shows it's associate. It's associative because it's defined as addition over the reals in each component. If you have three vectors A = (a,b,c), B = (i,j,k), C = (x,y,z), then if you have A + (B + C) you have (a,b,c) + ( (i,j,k) + (x,y,z) ) = (a,b,c) + (i+x,j+y,k+z) = (a+(i+x),b+(j+y),c+(k+z)) = (a+i+x,b+j+y,c+k+z). To be alternative, this must be equal to (A + B) + C, which will clearly yield the same result due to, as I said, associativity of addition over the reals. Therefore, vector addition is associative, QED. | |
Not exactly, just because you have a total of three vectors that doesn't instantly make something associate. I don't think you're judging the variables correctly.
| |
EmpirezTeam wrote:
Not exactly, just because you have a total of three vectors that doesn't instantly make something associate. I don't think you're judging the variables correctly. I'm pretty sure you're trolling and don't know what you're talking about. | |
Math makes my brain hurt.
| |
tl;dr
| |
METH!!!!!!!!!!!
| |
... I like math, when it has a purpose. But I don't understand the purpose of this.
It seems very much like common sense, as well, if I'm understanding it correctly. (I tend to visualize vectors as launchpads for objects - keep this in mind as I attempt to explain this.) Three objects all fire from the same distance toward the same center, at the same speed and with equal force. The force hits 0 as they reach the center. | |
A vector space is an abstraction of the notion of vectors. Vectors in a vector space need not represent any actual physical quantity. For example, the complex numbers can be viewed as a vector space with multiplication such that (a,b) x (c,d) = (ac - bd, ad + bc). Consequently, this vector space doesn't represent any physical system, but is simply an abstract algebra.
It also has an interesting property of being a normed division algebra over the reals, though it's non-unital (Unital means that, if you have some set S, there is an element I in S such that, for all A in S, A * I = A ), but it does have a weaker notion of identity. Hurwitz's theorem says there are only four unital algebras over the reals that are normed division algebras, and this algebra is an interesting result of there being a weaker notion of identity. | |