Ok, I guess I'm always confused why |S| on a set doesn't take the values into account, whereas |x| on a vector does take its values into account; how can mathematicians of all people be so inconsistent?
Mathematicians use inconsistent notations all the time. Symbols meaning slightly different things based on the type of the arguments are among the benign cases.
I stopped reading earlier, when they used superscript without explaining its meaning. Its clearly meant for someone with more domain expertise than me, with my hazy recollections of college math.