Is there colors that we can't see?

lol, we can't even accurately show Tyree purple, what makes you think we can show ones we can't see
 
This discussion is kind of tangent, because my point is not about single frequency colors.

But you also need to consider them, if you're counting colors.

Yes, but in the red-green range, the green cone perception goes up as the blue cone goes up, the blue doesn't add new frequency information. Same for red in the green-blue range. I admit, I'm not 100% certain of this. If you have a source, please link it.
For the red-green range you're right. However in the green-blue range you're not:

http://psy.ucsd.edu/~dmacleod/publications/61StockmanMacLeodJohnson1993.pdf
(figure 14 and 15)

Note that the absorbance for green and red cones merge and cross in the blue range.

So choose the colors that an artist chooses to use in an all-purpose digital pallet? I suppose that could work. Yeah, I'll say it: such an artist would choose to double his pallet, if his audience and him were granted a third receptor.

For best results it shouldn't be made digitally as that really limits the color space. But I'd say, that he wouldn't double the number of colors. It depends on how finely he grains his colors. If he used only very few colors before and mixed everything else, maybe he'd add only one or two. If he used many shades of colors before, he'd add a lot more than double.

It's not uncountable, there is just a lot of uncertainty in the count. And I have suggested a way to count colors.

If there is only a lot of uncertainity, you should be able to give a ballpark figure. How many colors do you think there are?

The article discusses limitations on the shape of the gamut, but no colors are mentioned as being impossible to display in the middle. Obviously the middle is limited by discretization, but since that can be programmed arbitrarily, it can be picked such that any specific color is possible. So I maintain that a monitor can be made to match the color of any low intensity laser perfectly.

Do you realise, that the colors in the middle are the mixed ones, while the single frequency ones are on the edges? That means, laser colors are can not be displayed unless the gamut shape matches perfectly the ideal shape at the edges.
 
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