What does finitely mean?
"Finitely" is an adverb describing something as limited, bounded, or countable — the direct opposite of "infinitely." It belongs almost entirely to the vocabulary of mathematics, logic, and theoretical computer science, where precision about whether a quantity is finite matters greatly. One speaks of a set containing "finitely many" elements, a group being "finitely generated," or an algorithm running in "finite time." The word derives from Latin finitus, meaning "finished" or "limited," the past participle of finire, "to end or bound." Though rare in everyday conversation, it is indispensable in technical contexts, since distinguishing the finite from the infinite underlies some of the deepest results in mathematics, from counting arguments to proofs about computability and the sizes of infinite sets.
adverbIn a finite manner; having limits or bounds, especially in size, extent, or number. In mathematics, it describes something that is bounded or countable rather than infinite.
- In a way that has limits or bounds; not infinitely (used chiefly in mathematics and logic, e.g. "finitely many").
"The set contains only finitely many elements."
"A computer can store only finitely much information."
"The group is said to be finitely generated if it arises from a finite set of elements."
Swap one letter and "finitely" becomes "finally" — a typo that turns 'at last' into 'bounded by mathematics.'
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of finitely
"Finitely" traces back to Latin finitus, the past participle of finire, meaning "to limit, bound, or finish," which itself comes from finis, "end or boundary." English adopted "finite" via Latin in the late Middle English period, with the adverb "finitely" forming later from it. The same root gives English a rich family of related words, including "define," "infinity," "final," and "finish," all preserving the core idea of an ending or boundary.
Related word forms
How finitely is actually used
"Finitely" is largely confined to formal, mathematical, and logical writing. Outside phrases like "finitely many" or "finitely generated," it rarely appears in everyday speech, where speakers prefer phrasings such as "only a limited number of."
Easily confused with finitely
"Finally" means at last or lastly, while "finitely" means in a bounded or limited way; they differ by one letter but share nothing in meaning.