continuous on

USAGE SUMMARY

The phrase "continuous on" is not correct in standard written English.
It is often used incorrectly; the correct term is "continuous in" or "continuous over" depending on the context. Example: "The function is continuous in the interval from 0 to 1."

⚠ May contain grammatical issues

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

where are continuous on.

Journal of Inequalities and Applications

Thus, is continuous on.

Boundary Value Problems

continuous on [0,T].

Probability, Uncertainty and Quantitative Risk

Then, is continuous on.

Journal of Inequalities and Applications

(1) is continuous on.

Journal of Inequalities and Applications

Obviously, is continuous on.

Boundary Value Problems

The map is continuous on.

Fixed Point Theory and Applications

where,, is continuous on,, exist, ;, ;.

Boundary Value Problems

(5) is weakly continuous on.

Journal of Inequalities and Applications

Thus is weakly continuous on.

Journal of Inequalities and Applications

(a) is weakly continuous on.

Fixed Point Theory and Applications

Expert writing Tips

Best practice

When describing a function's continuity, always use "continuous in" for intervals or regions, or "continuous over" for a domain. For example, "The function is continuous in the interval [0, 1]".

Common error

Avoid using "continuous on" as it is grammatically incorrect. The correct prepositions are "in" or "over", depending on the context. Using "continuous on" can make your writing appear less precise and unprofessional.

Linguistic Context

The phrase "continuous on" functions as an adjective phrase modifying a noun, attempting to describe the property of continuity over a specific domain. However, Ludwig AI indicates that this construction is not grammatically correct in standard English.

Expression frequency: Very common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Ludwig's WRAP-UP

While the phrase "continuous on" appears frequently in various contexts, particularly in scientific writing, Ludwig AI flags it as grammatically incorrect. The correct alternatives are "continuous in" or "continuous over", depending on whether you're referring to an interval/region or a domain, respectively. To ensure precision and credibility, especially in formal and scientific communication, it's best to avoid "continuous on" and opt for the grammatically sound alternatives. Using the proper prepositions maintains the clarity and professionalism of your writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

continuous in

Replaces the preposition "on" with "in" to achieve grammatical correctness when referring to a region or interval.

continuous over

Replaces the preposition "on" with "over" for correctness when referring to an area or domain.

maintains continuity on

Adds a verb to emphasize the action of maintaining continuity, slightly increasing formality.

exhibits continuity on

Similar to "maintains continuity", this highlights the presence of continuity as a characteristic.

remains continuous on

Focuses on the state of being continuously unchanged over a domain.

is consistently present on

Replaces "continuous" with "consistently present" to emphasize the persistent nature of the function or property.

preserves continuity on

Highlights the act of preserving continuity, implying an active process.

is uniformly continuous on

Specifies a stronger form of continuity, implying that the rate of change is bounded.

demonstrates continuity on

Similar to "exhibits continuity", but emphasizes the act of showing or proving continuity.

sustains continuity on

Emphasizes the act of keeping continuity in existence, suggesting that there are challenges to maintaining it.

FAQs

What is the correct way to say "continuous on"?

The correct way to express continuity is to use "continuous in" (for intervals or regions) or "continuous over" (for domains). For example, "The function is continuous in the interval [a, b]" or "The function is continuous over its entire domain".

Is "continuous on" ever correct?

In standard written English, "continuous on" is generally considered incorrect. The preferred phrasing is "continuous in" or "continuous over", depending on what you're describing.

What are some alternatives to saying something is "continuous on" a set?

Instead of "continuous on", you can say it is "continuous in" a set, or "continuous over" the set. Other options include "maintains continuity in" or "exhibits continuity over" the set.

Why is "continuous on" considered incorrect?

The preposition "on" typically indicates a surface or a direct relationship, which doesn't align with the mathematical concept of continuity over an interval or domain. "Continuous in" or "continuous over" more accurately convey the idea of continuity within or across a specified range.