chapter  1
Notation
Pages 1

For the nearest integers to a real number, x ∈ R, we use the standard notation for the ceiling and the floor,

x := min{n ∈ Z | n ≥ x}, x := max{n ∈ Z | n ≤ x},

and the sign σ(x) of a real number, x ∈ R, is defined by

σ(x) :=

{ 1 x ≥ 0, −1 x < 0. (1.1)

Furthermore, we denote the maximum and minimum of two numbers, x, y ∈ R, as

x ∨ y := max{x, y}, x ∧ y := min{x, y}.