Question about the intervals (b,b) and [b,b]

[AxiomOfChoice]

Let b be a real number. Correct me if I'm wrong, but it seems that:

(1) The interval (b,b) is empty, as are the intervals (b,b] and [b,b).
(2) The interval [b,b] consists of a single point (namely, b).

 

[Hurkyl]

Let b be a real number. Correct me if I'm wrong, but it seems that:

(1) The interval (b,b) is empty, as are the intervals (b,b] and [b,b).
(2) The interval [b,b] consists of a single point (namely, b).

These statements look correct to me.