Finitise

Finitise, with the American variant finitize, is a verb meaning to make finite or to impose a finite bound on a quantity, domain, or process. It is used in mathematics, logic, computer science, and data processing to describe transforming an object that is originally infinite or unbounded into a finite one, or enforcing finiteness through truncation, discretization, or bounding.

In mathematics and formal logic, finitising may refer to restricting attention to a finite substructure or to replacing an infinite model with a finite approximation that preserves certain properties. In computer science and data processing, it often means limiting inputs, buffers, or state spaces to a fixed size to ensure computability, resource bounds, or tractability. For example, a model might be finitised by restricting its domain to the first N elements, or a data stream might be finitised using a fixed-length window.

Etymology derives from finitude, with the suffix -ise (or -ize in American spelling), reflecting the action of making something finite. The term is niche and primarily found in technical or academic writing; it may appear as finitize in American texts and finitise in British contexts.

See also finitude, finite, finitary, finite model property, and related concepts of approximation and truncation. While not universally used, finitising provides a concise way to describe the deliberate reduction of infinite or unbounded constructs to finite representations for analysis, computation, or practical implementation.