Stars are often referred to as early or late types. "Early" is a synonym for hotter, while "late" is a synonym for cooler.
My lecture notes say:
O and B stars are sometimes referred to as ‘early-type’, while K and M are ‘late-type’.
If I look at a HR diagram, I see that main sequence O, B stars are hotter than main sequence K, M stars. So they are burning their fuel at a greater rate than K, M stars, so they run out of it early. So the stars which we are still able to observe now from the early universe are K, M stars, rather than O, B, which presumably formed rather *late**ly. Yet this is not consistent with the terminology above, so something is obviously wrong here.
What is wrong with my argument that the early and late words should be used in the other way round?