How do you convert set notation to interval notation?

Imagine we are to express [ a, b ] in set notation

A = [ a, b ], then A = { x ∈ R / a ≤ x ≤ b }

In this notation we define the characteristics of all x belonging to this set A ... x must be greater or equal to a and simultaneously smaller or equal to b ...

Interval notation is other way to say the same but assuming that means the extreme a is IN the interval and means extreme a is not.