Inkrementet

Inkrementet, or the increment, is a term used in mathematics and related fields to describe the amount by which a quantity changes when it increases from one state to another. It is commonly used to denote a finite, discrete change, as opposed to an infinitesimal change used in differential calculus.

In mathematics, consider a function f and an input change from x to x + Δx. The corresponding change in the output is Δf = f(x + Δx) − f(x), while Δx is the input increment. For example, with f(x) = x^2 and x = 3, Δx = 0.1 gives Δf = (3.1)^2 − 9 = 0.61. The linear approximation dy = f′(x)Δx, here f′(3) = 6, yields dy = 0.6, which is close to Δf for small Δx. The differential dy represents the idealized instantaneous rate of change, while Δf is the actual finite change.

In numerical methods, increments are used in finite difference schemes to approximate derivatives and integrate discrete systems. The step size h serves as the input increment, and the corresponding increments in the dependent variable form the basis of update formulas.

In physics, increments appear as small time steps Δt or distance increments Δs in discrete models and simulations.

In computer science, an increment often means increasing a variable by a fixed amount, typically one, as in x = x + 1 or x++. The concept is central to counting, loops, and iterative algorithms.

Etymology traces inkrement from Latin incrementum, with cognates in several languages where the definite form inkrementet denotes “the increment.”