Arthraxium wrote:
Are we done?
We are most certainly not done. You haven't even defined f(x)! As near as I can tell, you intend for f(x) to be a many-valued function that takes on as values all maps with star ratings equal to the argument. From there, we have to define some sort of ordering on the set of maps in order to make sense of the interval. I guess the obvious choice is to consider all maps of the same star rating to be members of an equivalence class and then using the standard total order on real numbers over the star rating associated with each equivalence class.
However, I'm not entirely sure that this is what you meant because it raises some questions about your choice of notation. For one thing, I wonder why you would have chosen to use f(x) as boundaries of your interval, rather than choosing an interval for x and then indicating that we were accepting all f(x) for all x in that interval. It also makes me wonder why you used the limits, when you could, assuming I had correctly interpreted your notation, just as easily have chosen f(4) to be the lower limit and f(6) to be the upper limit. Your choice to use limits makes me think there must be some sort of discontinuity at x=4 and x=6 and it's not clear to me what would cause that to happen. Even more baffling is your choice to use one-sided limits. I honestly have no idea what quantity you could have had in mind that would have different limits from the left and the right that would make sense in the context in which you used them.
When we've sorted all of that out, we can get back to the very important argument taking place in this thread over trivial details.