Interval: meaning, definitions and examples

mathematical

An interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. Intervals can be open (not including the endpoints), closed (including the endpoints), or half-open (including one endpoint but not the other).

range, scope, span.

Which Synonym Should You Choose?

Word	Description / Examples
interval	Used to describe a period of time between events or a physical space between objects. It's often used in contexts like scheduling, time management, and measurements. There was a ten-minute interval between the first and second acts of the play. The intervals between the columns were evenly spaced.
range	Used to refer to the distance between the lowest and highest points in a set of data, capabilities, or choices. Commonly used in contexts like mathematics, data analysis, and descriptions of variety. The temperature range this week is between 50 and 70 degrees. The store offers a wide range of products.
span	Used to describe the full reach or length of something, especially in terms of time or space. Often used in historical contexts, personal achievements, and architectural measurements. Her career spanned more than four decades. The bridge spans the river at its widest point.
scope	Used to indicate the extent or range of a subject covered by a book, program, discussion, etc. Frequently used in academic, project management, and work-related contexts. The scope of the research includes both qualitative and quantitative analysis. We need to define the scope of this project clearly.

Examples of usage

• The interval (0, 1) includes all real numbers between 0 and 1, but not 0 and 1 themselves.

• The interval [2, 5] includes all real numbers from 2 to 5, including 2 and 5.

time

An interval refers to a period of time between two specified points or events. It can be a short interval, like a few minutes, or a longer interval, like a decade.

Examples of usage

• There was a brief interval between the two acts of the play.

• The intervals between meals are important for digestion.

music

In music theory, an interval is the difference in pitch between two notes. Intervals can be classified as major, minor, perfect, augmented, or diminished, depending on the number of half steps they contain.

Examples of usage

• The interval between C and E is a major third.

• The song uses a variety of intervals to create tension and resolution.