defined on

USAGE SUMMARY

The phrase "defined on" is correct and usable in written English.
It is typically used in mathematical or technical contexts to indicate the domain or set over which a function or concept is applicable. Example: "The function f(x) is defined on the interval [0, 1]."

✓ Grammatically correct

Science

News & Media

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

For, let the function be defined on as follows: (2.11).

Journal of Inequalities and Applications

(A lunk is defined, on a poster, as "one who grunts, drops weights, or judges").

The New York Times

Vegetation zones are well defined on both islands.

Encyclopedia Britannica

Our stance is also clearly defined on www.explorebeef.org.

The New York Times

This season, the C.I.A. will largely be defined on television by "The Agency".

The New York Times

This might put journalism, broadly defined, on a much more stable foundation".

The New York Times

Oklahoma State had its motivation defined on a ghastly night of tragedy.

The New York Times - Sports

defined on.

Journal of Inequalities and Applications

(H3) defined on satisfies (14).

Advances in Difference Equations

defined on infinite-dimensional simplex.

Advances in Difference Equations

be defined on S n.

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When using "defined on" in mathematical or technical writing, ensure that you clearly specify the domain or set to which the definition applies to avoid ambiguity.

Common error

Avoid using "defined on" without explicitly stating the set or domain. For example, instead of "The function is defined on", specify "The function is defined on the interval [0, 1]".

Linguistic Context

The phrase "defined on" primarily functions as a prepositional phrase specifying the domain or set over which a particular function, concept, or model is applicable. It provides essential context by indicating the scope and boundaries of the definition. Ludwig shows several examples where a function or variable is "defined on" a specific mathematical space.

Expression frequency: Very common

Frequent in

Science

68%

News & Media

16%

Encyclopedias

3%

Less common in

Formal & Business

1%

Wiki

1%

Social Media

0%

Ludwig's WRAP-UP

The phrase "defined on" is a grammatically correct and very common prepositional phrase primarily used in formal and scientific contexts. As confirmed by Ludwig AI, it serves to specify the domain or set over which a concept, function, or model is applicable. Its primary function is to establish clarity and precision in technical writing, ensuring that the scope of a definition is well-understood. While its usage is concentrated in scientific publications and academic papers, understanding its function and purpose is crucial for clear communication in technical domains.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

specified for

Indicates a particular specification or purpose for which something is intended.

applicable to

Highlights the relevance or suitability of something in a specific context.

valid in

Implies that something holds true or is correct within certain boundaries or conditions.

based upon

Emphasizes the foundation or rationale behind a definition or concept.

contingent on

Suggests a dependence or condition that must be met for something to be true.

predicated on

Indicates that something is founded or based on a particular assumption or premise.

restricted to

Highlights the limitations or boundaries of a definition or concept.

conditioned by

Indicates that something's state or nature is influenced by particular circumstances.

determined by

Highlights how something is shaped or influenced by certain factors.

dependent on

Similar to contingent on, but emphasizes reliance on something else.

FAQs

How can I use "defined on" in a sentence?

The phrase "defined on" is used to specify the domain or set over which a function or concept is applicable. For example, you might say "The function is defined on the interval [0, 1]" or "The model is defined on a regular lattice".

What are some alternatives to "defined on"?

You can use alternatives such as "specified for", "applicable to", or "based upon" depending on the specific context.

In what contexts is "defined on" most commonly used?

"Defined on" is frequently used in mathematical and technical writing to specify the domain of a function, model, or concept. Ludwig AI examples show it is used in Science, News & Media and Encyclopedias.

Is it grammatically correct to use "defined on"?

Yes, "defined on" is grammatically correct and widely used, especially in mathematical and technical contexts.