I have to wonder why a relation algebra language isn't actually algebraic. What about projections in the form of something like c := a x b etc? Nooo, they had to make it look like COBOL.
In databases class, they used Pi for projection, bowtie for natural join, and sigma for row filtration. They added conditions on the operators with subscripts. SQL is just the standardized version of that.
"Standardized"...and without the legibility of symbolic notation and the option to use intermediate named relvars?
It's designed to be "natural", meaning that technical symbols were largely avoided. Someone who knows little about formal notation but a decent amount about databases can usually figure out what's going on. It's also easier to type, seeing how most of the relevant symbols aren't on your average keyboard.
I have seen it taught with operators like that.
Because one of SEQUEL, and thus SQL's design goals was to create a language that's usable by non-programmers of various levels of computer and math fluency. Having to remember a set of symbols just to get a jobs report would be a huge turn-off to a huge subsection of people that the language was intended for.