Quick convention question

Is the closed interval [a,a] considered a legitimate notation for the set {a}? Would (a,a) denote the empty set?

 

A={x : f(x)<0 on [a,x]}
Is a in A? It is if f(x)<0 on [a,a]. And since [a,a] has only one number, it suffices to show that f(a)<0.

A={x : f(x)<0 on (a,x)}
Is a in A? It is if f(x)<0 on (a,a). But this is kind of nonsense. There is nothing in (a,a). You make the call.

So anyway, I just wanted to point this out to show why you might write (a,a) rather than {}.