are defined to be

USAGE SUMMARY

The phrase "are defined to be" is correct and usable in written English.
It is typically used in formal or academic contexts to specify the meaning or parameters of a term or concept. Example: "In this study, the terms 'success' and 'failure' are defined to be the outcomes of the experiment based on the criteria established."

✓ Grammatically correct

Science

Academia

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Results are defined to be significant at p < 0.05.

Nature

Often the elastic and dielectric coefficients are defined to be constant for the sake of simplicity.

International Journal of Solids and Structures

Optimum conditions are defined to be 210 230 °C and 200 210 °C for PBT and PA6 respectively.

Composites Part B: Engineering

Thirdly, to reliable discriminate people, specific depth-based features are defined to be used with a Real AdaBoost classifier.

Energy and Buildings

Hot pixels and columns are defined to be those which produce a spuriously high or saturated pulse-height for a large number of consecutive frames of data.

Harvard University

Events are defined to be independent if they occurred at separate sampling sites or if there was at least a 24-h time lapse between the end of a precipitation event and the beginning of the next one.

Nature

Of a particular interest are free Krieger algebras, which, by analogy with crossed products and ordinary Krieger factors, are defined to be algebras of the form Φ(L∞[0, 1], η).

Journal of Functional Analysis

Acoustic Bessel Bullets (BB) are defined to be a new class of band-limited Transient Bessel Beams or localized waves which maintain their shape and amplitude as they propagate in space.

Journal of Sound and Vibration

The random variables X and Y are defined to be independent if the events {X = xi} and {Y = yj} are independent for all i and j i.e., if h xi, yj) = f xi g yj) for all i and j.

Encyclopedia Britannica

Generalized incomplete Trojan-type designs are defined to be row column designs in which each cell, corresponding to the intersection of row and column, contains more than one treatment and the rows are incomplete.

Statistics & Probability Letters

In VAN a common open platform and common means for classical fieldbus tasks and telecontrol tasks are defined to be able to realise Virtual Automation Networks that combine both fielbus and telecontrol related aspects.

IFAC Proceedings Volumes

Expert writing Tips

Best practice

When using "are defined to be", ensure the definition is clear, concise, and consistent with the context.

Common error

Avoid using overly complex language when defining terms. The goal is clarity, so strive for simplicity and directness in your definitions.

Linguistic Context

The phrase "are defined to be" functions as a linking verb phrase. It connects a subject with a definition or description. Ludwig AI data supports this function, indicating frequent use in defining terms and concepts.

Expression frequency: Very common

Frequent in

Science

75%

Academia

15%

Encyclopedias

5%

Less common in

News & Media

2%

Formal & Business

1%

Wiki

2%

Ludwig's WRAP-UP

In summary, "are defined to be" is a linking verb phrase primarily used to introduce formal definitions. Ludwig AI analysis confirms that it is grammatically sound and frequently employed in academic and scientific contexts. While alternatives like "are considered to be" and "are known as" exist, "are defined to be" maintains a strong presence in formal writing. When using this phrase, ensure clarity and precision in your definitions to avoid ambiguity. As such, using "are defined to be" is often the most precise and reliable choice for establishing definitions.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

are considered to be

This alternative shifts the focus to perception or judgment rather than strict definition.

are known as

This alternative emphasizes common recognition or naming conventions.

are understood as

This alternative highlights interpretation or comprehension.

are characterized as

This alternative focuses on key features or qualities.

are identified as

This alternative emphasizes recognition or categorization.

are designated as

This alternative suggests formal appointment or assignment.

are classified as

This alternative focuses on systematic arrangement or grouping.

are regarded as

This alternative expresses a particular opinion or assessment.

can be described as

This alternative offers a descriptive perspective.

can be interpreted as

This alternative suggests a specific reading or understanding.

FAQs

How to use "are defined to be" in a sentence?

Use "are defined to be" to introduce a formal definition of a term or concept. For example, "In this context, 'success' and 'failure' "are defined to be" the outcomes of the experiment based on established criteria."

What can I say instead of "are defined to be"?

You can use alternatives like "are considered to be", "are known as", or "are understood as" depending on the context.

Which is correct, "are defined to be" or "is defined as"?

"Are defined to be" is used for plural subjects, while "is defined as" is used for singular subjects. For example, "The terms "are defined to be"..." versus "The term "is defined as"...".

What's the difference between "are defined to be" and "are described as"?

"Are defined to be" implies a precise and formal definition, while "are described as" suggests a more general or descriptive characterization.