difference

Difference is the property of being unlike or the result of comparing two quantities. It is used to express how much one thing varies from another, often in terms of magnitude or attributes. In mathematics and related fields, difference has several formal meanings.

In arithmetic, the difference between two numbers is the result of subtracting one from the other. The order matters: the difference a − b is the amount by which a exceeds b, and it can be negative if a < b. The absolute difference |a − b| is the nonnegative distance between the numbers.

In set theory, the difference (A \ B) consists of elements that belong to A but not to B.

In geometry and vector algebra, the difference between two points or vectors is their subtraction, yielding a vector indicating direction and displacement.

In calculus and numerical analysis, finite differences approximate derivatives and are used in discrete models. The forward difference Δf(n) = f(n+1) − f(n) is a common example.

In everyday language, difference also refers to qualitative distinctions, such as contrasts in color, form, or behavior, and to how two entities vary in attributes.

In computing, “diff” is a tool and concept for comparing files to show insertions, deletions, and changes.

The term is often contrasted with similarity, sameness, or convergence. Understanding difference requires specifying the two items being compared and the context of the comparison.