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.