If you had a set of 1000 cards, where 495 have color 0x00000000 +- x and 495 have color 0xFFFFFFFF +- x and a further 10 have color Rand(0x00000000, 0xFFFFFFFF)

If you had a set of 1000 cards, where 495 have color 0x00000000 +- x and 495 have color 0xFFFFFFFF +- x and a further 10 have color Rand(0x00000000, 0xFFFFFFFF) and you had to categorize these, if x is very small, you would probably end up with three sets ... 0, F, and some R, where the 0 set would get everything that is 0x00000000 or close to it, F set would be 0xFFFFFFFF and everything close to that, and then some R which is in the space outside those sets. But if the vast majority of samples are in 0 and F, then it makes sense to have these as categories to study, without invalidating the fact that there is another set R which defies clean placement into either. But pretending like 0 and F aren't categories, but rather everything is a smooth linear continuum seems silly too if x is small.