Those who teach special relativity consider it a very important exercise to have students decide how to measure the length of a rapidly moving object. That's religious indoctrination and a wrongheaded approach to physics. The theoretical process that physicists talk about to measure the length...
This post is a sincere request for help. I assume that the following problem can be represented by a differential equation and that only a mathematician can solve it.
Let A={real numbers x such that |x|<1}
Let S={real numbers Z such that 1 < Z < infinity}
Define ^ on A by the rule x^y...