[AlotOfReading]

They're not series, that's just a convenient way to think about defining and calculating them. I've never found it particularly useful to deal with the series definitions either, and none of the (good) approximation methods I'm aware of actually take that approach.

Moreover, EML is complete in a way that your suggested function isn't: If you take a finite combination of basis functions, can it build periodic functions? Hardy proved over a century ago that real (+,-,/,*,exp,ln) can't do this (and answering the paper's unresolved question about similar real-valued functions in the negative). EML being able to build periodic functions is a lot less surprising for obvious reasons, but still pretty neat.

[scotty79]

EML goes through complex numbers and infinities internally.

Previous commenter meant that there are infinite series inside log and exp.

To achieve a thing like sin(x) from his universal expression, yes you'd need infinite series of those, not a finite set of operations, but to get all 36 basic function you'd need a finite set of different infinite series.

So exp and log just happen to be the labels for two element set of such infinite series that you'd have to use to make 36 functions out of the operator that pervious commenter proposed.

All that said, I still think it's pretty neat too.