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Better Derivative: Division in a Two-Step Limit Process
Let te 3-vector of the differential element go to zero first, followed by the scalar.
For
R
, imaginary part is zero.
For
C
, free to change order of limits.
For
H
, not free to change order.
Complex numbers are symmetric for time and 1-space. Quaternion 3-space breaks the symmetry with time, so the order of limits matters.
sweetser@alum.mit.edu copyright 2003, all rights reserved.
