You CANNOT interpret a color upon seeing UV or IR. The human brain doesn't have a color mapped to them, because the eye isn't sensitive to them.
The sun's peak emissions are in the visible light spectrum. Our eyes adapted to see the peak emission of the sun, because those are the colors most abundant during our evolution, and thus those are the only colors needed to survive.
If you only see pure UV or pure IR...it will look black and you'd see nothing.
Only in false-color displays can they actually have a color. And all that is, is the device re-mapping the image and re-emitting a different image (containing the same information) in the visible spectrum.
There are general conventions to mapping the non-visible to visible. I don't know the conventions off the top of my head...but of course there are some false-color displays that "make up" their own convention.
"how many ultraviolets/infrareds are there?"
You seem to be fixated on a countable number of colors in the visible spectrum. This isn't true at all.
You only think there are seven colors (or six or eight, depending on how much you know about color), because human vision is able to distinguish them (with our three cone cell receptors, each selectively sensitive to different ranges of the spectrum).
The actual spectrum is completely continuous, with no definite boundary existing between any pair of colors.
In other words...red and green are obviously different.
In between red and green, there is a secondary color called yellow, which stimulates both the red-type cone and the green-type cone.
Now...you can distinguish yellow from green, and yellow from red.
BUT, now let's try to look at the distinction of red and yellow.
Well...the transitional color there is of course orange.
What's between orange and yellow? Yellow orange.
What's between yellow-orange and yellow? Yellowish yellow-orange.
What's between yellowish yellow-orange and yellow? Yellowish yellowish yellow-orange.
I can go on and on.
Either way, my point still stands. The spectrum is continuous. There are an uncountable number of possible colors just within the visible spectrum.
IR and UV are just as continuous...if not, moreso.
You don't have sensors that are uniquely sensitive to different zones of UV or IR...it all seems to be the same stuff in the ways that you might "feel" it to be.