A mathematical interval is a special set of individual real numbers.

The Claim

In standard high-school mathematics and set theory, a set such as A is defined as a collection of individual elements rather than as a single interval object.

Verified by Lenz · Sep 10, 2026

The Short Version

Standard mathematics defines a set as a collection determined by its elements or members. An interval is not an alternative general definition of a set; it is a particular kind of set, usually a subset of the real numbers. A set may still be treated as one unified mathematical object without ceasing to be composed of elements.

Caveats

Some sets are intervals, so the contrast concerns the general definition rather than mutually exclusive categories.
A set is also treated as a single unified mathematical object, despite being characterized by its elements.
The notation “A” alone does not indicate whether the set is an interval.