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.