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Yes, a brilliant pure emerald green cannot be achieved. The question of what particular color is actually displayed is much more complicated - was it sensed correctly by the input device? What color within the range of reproducible colors should it be translated to? In your case, the over-all system result moved its hue toward yellow. A correct hue (but with reduced saturation) might be more desirable. These considerations are of very practical importance when the color monitor is being used to represent some other reproduction device, such as the restricted range of newspaper inks. It is generally considered less important for the cases of objects that are outside the range of the monitor, since these are normally man-made and not likely to be a concern in ordinary pictures of scenes and people.
This is the subject of color managment systems. When dealing with these issues in Photoshop, for example, you may choose a working color space, and colors outside the range will be indicated on the monitor. Photoshop has a wider-range choice than sRGB, but the input device also has to support it, of course.
Colors that are unreproducible have to be translated to something, and this will be determined by the "rendering intent", a choice of an algorithm that maps input to output colors. For example,the rendering may compress mainly the colors that are outside the range, or it may compress all colors in some way so that their relative saturation percentage is maintained, etc. etc. It is not only the hue and saturation that have to be accomodated, but the brightness or density range. Reflective objects generally can have high saturation at low brightness but not at high brightness, while CRTs can have high saturation at high brightness, but not at low brightness (due to stray light reflectance).
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