Interval Notation

Need homework help? Connect with our top Interval Notation Experts!

Interval Notation

Interval notation is a method of representing a set of real numbers by combining symbols and numbers. It is normally used in mathematics to represent the set of all real numbers that a function or variable can accept.

The three main types of intervals are:

Open intervals: An open interval is a set of real numbers that consists of all the numbers between two given values, but excludes the values themselves. It is marked using parentheses, such as this: (a, b). As an example, the open interval (2, 5) denotes all numbers between 2 and 5, excluding the 2 and 5 themselves.

Closed intervals: A closed interval is a set of real numbers that consists of all the numbers between two given values, and also the values themselves. It is marked by square brackets, like this: [a, b]. As an example, the closed interval [2, 5] denotes all real numbers between 2 and 5, and also the 2 and 5 themselves.

Half-open intervals: A half-open interval is a set of real numbers that consists of all the real numbers between two given values, but only retains one of the values itself. It is marked by both parentheses and square brackets, like this: (a, b] or [a, b). As an example, the half-open interval (2, 5] represents all real numbers between 2 and 5, and also 5, but leaves 2.

In interval notation, the use of the symbols "-infinity" and "infinity", is also possible to depict negative and positive infinity, respectively. As an example, the interval (-infinity, 5) denotes all numbers that are less than 5, and the interval [2, infinity) denotes all numbers greater than or equal to 2.

Interval notation is a straightforward and very efficient way to represent sets of real numbers, and it is frequently used in mathematics and other fields to represent data or value ranges.

Browse More Topics

Volume of a Cylinder Surface Area of a Cylinder How to Convert Ounces to Gallons Volume of a Cone Area of the Triangle Domain and Range Volume of a Sphere Lines, Line Segment and Rays Axis of Symmetry of a Parabola Volume of a Pyramid Surface Area of Pyramid Geometric Series 30-60-90 Triangles Distance Formula Sum and Difference of a Cube Degree to Radian Measure Coplanar Graphic Square Root Functions 45-45-90 Triangle Graphing Cosine Function Surface Area of a Prism Radian to Degree Mean, Median, and Mode Powers of 10 Rounding Decimals Converse Inverse and Contrapositive Surface area of a cone Vertex of a Parabola Surface area of a sphere Decimals Reflections Fractions to Percent One-to-One Function Graphing Logarithmic Functions Quadrilaterals Absolute Value Function Law of Sines Weight Mass Law of Cosines Tangent Function Prime and Composite Number Linear Pair Complementary Angles Supplementary Angles Reflective, Symmetric, and Transitive Properties Rate of Change Volume of a Prism Completing The Square End behavior of Function Vertical Angles

30 minutes Live Session FREE!