For x ∈ ℝ, let ⌊x⌋ denote the greatest integer less than or equal to x.
For x, y ∈ ℝ, define
min{x,y}={ x yif x≤y,otherwise.Let f:[−2𝜋, 2𝜋] → ℝ be defined by
f(x) = sin(min{x, x − ⌊x⌋}) for x ∈ [−2𝜋, 2𝜋].
Consider the set S = {x ∈ [−2𝜋, 2𝜋]: f is discontinuous at x}.
Which one of the following statements is TRUE ?