finitely
C2Pronunciation
UK
- /fˈaɪnaɪtlɪ/
US
- /fˈaɪnaɪtli/
Description
- With limits
- Not endlessly
- In a limited number of ways
- Within clear bounds
- In finite amount
"Finitely" describes something that exists or happens within a limit. Think of counting apples. You can have finitely many apples because there is a stopping point, even if the number is very large. It is most often used in mathematics and computer science to describe sets, steps, or processes that do not go on forever. If you have finitely many cookies in a jar, you will eventually run out. While space may or may not be infinite, the number of pages in a book is finite.
The word is the adverb form of "finite," which means having limits or bounds. When we use "finitely," we are usually stressing that something is not endless. You would not usually hear it in daily talk, but it is natural in careful writing, especially when someone wants to say that the number of items or steps is limited.
"Finitely" means in a way that has a limit. It tells you that something does not continue forever and does not exist in an endless amount. The word is mainly used to contrast with "infinitely," which points to something without any end or boundary. While "finite" appears more often in everyday English, "finitely" is more specialized and is common in math, logic, and computer science.
This word is especially common when people talk about number, structure, or repetition. For example, you might read that there are "finitely many solutions," "finitely many states," or "finitely many steps." In each case, the point is not that the number is small, but that there is some final number. It could be three, three thousand, or far more, as long as it is not endless.
In general writing, "finitely" often appears before words like "many" or in fixed technical phrases. A sentence such as "There are only finitely many ways to arrange these tiles" sounds natural. By contrast, a sentence like "The project was funded finitely" sounds wrong, because English usually uses "finite" in that idea instead, as in "for a finite period" or "with finite resources."
It is important to remember that "finitely" does not mean "small." A very large number can still be finitely large if it has an upper limit. When you see this word, think of a boundary, an ending, or a total that can in principle be reached. That is why the word is useful whenever someone wants to make it clear that something is limited rather than endless.
Examples
- 1
State machines
The machine can be in only finitely many states.
- 2
Finite process
If the process always gets smaller, it must stop after finitely many steps.
- 3
Group theory
The paper focuses on finitely generated groups.
Domain
in mathematics, finitely generated
built from a limited set of basic elements
Forms and spellings
1 form open this card.
Main spelling
- finitelyadverb