Inkremente

Inkremente (singular Inkrement) is a term used in mathematics, computer science, and related fields to denote a small change or step in a quantity. An increment is the amount by which a variable increases between successive states or measurements. In many contexts increments are called Δx, Δt, or simply an additive amount.

In mathematics, increments are used to describe finite differences in sequences or functions. For a sequence {a_n}, the increment from a_{n-1} to a_n is a_n − a_{n-1}. In calculus, derivatives are defined as limits of ratios of increments as the increment tends to zero.

In programming, the term is common for operations that increase a variable's value. The increment operator, found in many languages, takes forms such as i++ (post-increment) or ++i (pre-increment), increasing i by one; more generally i += k adds k. Increments are frequently used to implement loops, counters, and iterators.

In numerical methods and modeling, step sizes or increments, such as Δt in time integration or Δx in spatial grids, determine the resolution and stability of simulations. Choosing appropriate increments is essential for accuracy and convergence.

Etymology: Inkrement comes from Latin incrementum via German, with Inkremente as the plural. The term is used in German-language technical writing and in bilingual contexts to translate the English "increment" or "step."