MetalMario201 wrote:
Let Y be some subset of X such that A = B ∖ Y
Assuming that there still are bad things that can be done in a map that hasn't been done yet (in other words, assuming that B does not completely cover X)
A Vann diagram like the above can be drawn. (It is obvious that A is a subset of B, since B is the set of ALL beatmaps.)
Here, you can easily see that no subset of X (call it Y) can satisfy A = B ∖ Y
Since there are elements of B that X does not cover, it is impossible for a subset of X to leave only A after being subtracted from B.The result is the same when you assume that B does completely cover X.
It is by common sense that X cannot completely cover B.Therefore, no such subset Y can exist.
In this argument I have assumed that A ∖ B is the same as A - B. If that is not the case, please kindly explain what the symbol ∖ means, and I will have another go at the problem. Being an Asian, I've never seen the symbol ∖ being used
EDIT : Oh shit I didn't notice there was a page 2. Damnit.