RCA - Real

The union, A or B, is the set defined by

A ∪ B = { x∈X : x∈A or x∈B}

The intersection, A and B, is the set defined by

A ∩ B = { x∈X : x∈A and x∈B}

A and B are disjoint if

A ∩ B = ∅

Let A be a subset of a set X. Then, the complement of A in X, A^c (also X −A or X\A) is the set

A^c = { x∈X : x/∈A}

Real Function Definition

Suppose that X ⊆ R. A real function f : X → R is a rule which assigns to every real number x ∈ X a unique real number y ∈ R. If the number y ∈ R corresponds to the number x ∈ X, then we write y = f(x)

The Euclidian Distance on R

The function d : R×R→[0,∞) defined by: d(x,y) = |x−y|, ∀ x, y ∈ R.