Base units - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: Base units (/showthread.php?tid=1147) Base units - Xorter - 01/22/2017 A few days ago, I post a question about the derivatives of these units. But to do it, I need to know everything about base units. I think this forum is optimal to collect our knowledges of it. So a multidimensional number is from a linear combination of these units, We multiply them like this way: $i_x i_y = \eps _{ijk} i_{x\^k}$ where i!=j, $\eps$ is the levi-civita tensor which gives the sign of the multiplication, and ^ is a logic binary operator: xor. And of course, we can represent them as matrices, too ... But just from reals to quaternions, because of the non-associativity of the octonions, the multiplication of the matrices of the representation of these octonions does not work ... I do not know why. (?) I have many questions: Why cannot we represent the octonions, sedenions ... etc.? What is the derivative of $i_x$? What is $i_x^{-1}$ (inverse)? Which logic binary operators could we substitute instead of $\eps _{ijk}$? What is the taylor series of the xor and the levi-civita ops? How can we calculate with i[x] where x is not integer, so it is real or complex?