Numerical Intervals

Let′s take two numbers a and b such, that a<b and point on the coordinate line corresponding points.

The set of all numbers x, that satisfies the inequalities a<x<b , designates (a,b) and called the interval.

The set of all numbers x, each of which satisfies the inequalities   a<=x<=b , designates [a,b ] and called the segment.

The interval and segment are finite numerical intervals. There are two types of finite numerical intervals:[a,b) is the set of the numbers x, that satisfies the inequalities a<=x<b, and (a,b] is the set of the numbers x , that satisfies the inequalities a<x<=b. These intervals is called half-interval.

There are infinite number intervals. The set of all numbers x, that satisfies the inequality x>=a designate as [a,+oo) and called ray and the set of all numbers x, that satisfies the inequality (a,+oo) is called open ray.

The sign "+oo" read as "plus infinite".

Analogically, let′s consider the ray of type (-oo,b] (numbers, that satisfies the inequality x<=b ) and the open ray of type (-oo,b) (numbers, that satisfy the inequality x<b). The sign "-oo " read as: "minus infinite".

In practice, we don′t always use the terms "interval", "segment", "half-interval", "ray" replacing them with the common term numerical interval.