finite set

USAGE SUMMARY

"finite set" is a correct and usable phrase in written English.
It is used to describe a set of items that has a limited and predetermined number of elements. For example, "The finite set of numbers from 1 to 10 determine the range of possible answers for this math question."

✓ Grammatically correct

Science

News & Media

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Properties of finite set systems.

Yale University

Well, he's merely showing you a finite set of swans.

The New York Times

containing values from a finite set of constants.

University of California, Berkeley

With a fixed and finite set of value, the only question is how to allocate it.

Harvard Business Review

These prioritizations were not driven by the need to complete a finite set of tasks.

Harvard Business Review

But this finite set is consistent, as is seen by taking ξ = 1/(n + 1).

Encyclopedia Britannica

Either way, a finite set of primes can always be augmented.

Encyclopedia Britannica

But even in the structure of the music, a finite set of options holds steady.

The New York Times - Arts

A finite set is nonequivalent to each of its proper subsets.

Encyclopedia Britannica

where is a finite set.

Journal of Inequalities and Applications

Let be a finite set.

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When using "finite set", ensure the context clearly indicates that the number of elements is both limited and countable. This avoids ambiguity and ensures accurate communication, especially in technical or mathematical writing.

Common error

Avoid using "finite set" when you actually mean a countable but potentially infinite set. A finite set has a definite, limited number of elements, while a countable infinite set can be put into a one-to-one correspondence with the natural numbers, even if it never ends.

Linguistic Context

The phrase "finite set" functions as a noun phrase, often acting as a subject or object in a sentence. Ludwig examples demonstrate its use in defining mathematical concepts and describing constrained collections. It specifies a set with a limited, countable number of elements.

Expression frequency: Very common

Frequent in

Science

53%

News & Media

17%

Encyclopedias

15%

Less common in

Academia

5%

Wiki

3%

Formal & Business

2%

Ludwig's WRAP-UP

In summary, "finite set" is a grammatically correct and commonly used phrase that refers to a set with a limited and countable number of elements. Ludwig AI confirms its validity and prevalence in various contexts. While it appears most frequently in scientific, news, and encyclopedia contexts, it can be used more broadly to indicate a limited collection. When using this phrase, it's important to ensure the context clearly shows the limitation and countability of elements, differentiating it from countable infinite sets. Alternatives like "limited set" or "bounded set" can be used depending on the specific nuance you want to convey. The phrase is a valuable tool for precise communication, particularly in technical and mathematical fields.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

Limited set

Emphasizes the restriction on the number of elements.

Bounded set

Focuses on the constraint of the set's extent or size.

Discrete set

Highlights the separateness of elements within the set.

Fixed set

Indicates that the set is unchanging and definite.

Determinate set

Stresses the precisely defined nature of the set.

Circumscribed set

Highlights the set being confined within certain limits.

Constrained set

Indicates limitations or restrictions on the set's contents.

Restricted set

Focuses on the limitations imposed on the set's elements.

Defined set

Suggests a clear and established boundary for the set.

Enumerated set

Highlights the possibility of listing the set's elements completely.

FAQs

How is "finite set" used in mathematical contexts?

In mathematics, "finite set" refers to a set that has a limited number of elements. This means you can count the elements and arrive at a definite number. It's contrasted with an "infinite set", which has an unlimited number of elements.

Can "finite set" be used outside of mathematics?

Yes, the term "finite set" can be used in any context where you want to emphasize that a collection is limited in size. For example, "The project has a finite set of tasks" means there's a specific number of tasks to complete.

What are some alternatives to "finite set"?

Depending on the context, you can use alternatives like "limited set", "bounded set", or "fixed set". These phrases convey a similar idea of a restricted collection.

Is there a difference between "finite set" and "finished set"?

While "finished set" might imply that a set is complete, "finite set" specifically refers to the number of elements in the set. A set can be finite without being 'finished' in the sense of being complete for a particular purpose. The phrase "finished set" is not a standard mathematical term.