are defined below

USAGE SUMMARY

The phrase "are defined below" is correct and usable in written English.
It is typically used to indicate that specific terms or concepts will be explained or clarified in the following text. Example: "The key terms used in this document are defined below to ensure clarity and understanding."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

59 human-written examples

They are defined below.

European Transport Research Review

These metrics are defined below: RD function.

EURASIP Journal on Advances in Signal Processing

The contextual approximations are defined below.

Journal of the Brazilian Computer Society

The assessment criteria are defined below.

EURASIP Journal on Image and Video Processing

These two quantities are defined below.

EURASIP Journal on Wireless Communications and Networking

Continuous and dashed vertical lines are defined below Figure 2.

Chemistry Central Journal

The three main objectives of multivariate data analysis are defined below: 1.

EPJ Techniques and Instrumentation

The variables of Eq. (3) are defined below, while data sources are explained in the Appendix.

Journal of Economic Structures

A few fundamental and recurring terms of this paper are defined below.

Environmental Systems Research

The concepts of convergence, Cauchy sequence and completeness in a RMS are defined below.

Fixed Point Theory and Applications

The variables x ℓ′ and (bar {u}_{l}') denote tentative variables and are defined below.

EURASIP Journal on Advances in Signal Processing

Expert writing Tips

Best practice

When using "are defined below", ensure that the definitions are clear, concise, and directly relevant to the context. This helps maintain the reader's understanding and avoids ambiguity.

Common error

A common mistake is to use the phrase "are defined below" but then fail to provide the definitions or explanations. Always double-check that the subsequent text contains the promised information.

Linguistic Context

The phrase "are defined below" serves as an introductory phrase to indicate that terms, concepts, or variables will be explicitly defined in the subsequent text. Ludwig AI confirms this usage through numerous examples across various domains.

Expression frequency: Very common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, the phrase "are defined below" is a very common and grammatically correct introductory phrase, predominantly used in formal and scientific writing. Its main function is to explicitly signal that the definitions of certain terms will be provided in the following text, ensuring clarity and avoiding ambiguity. Ludwig AI's analysis, supported by numerous examples, shows the phrase's consistent use in academic and technical contexts. To enhance your writing, always ensure that the promised definitions are actually provided and are clear and concise. Alternatives like "are explained below" or "are detailed further below" can be used for variety, although "are defined below" remains a direct and effective choice.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

are explained in detail below

Replaces "defined" with "explained in detail", emphasizing a more comprehensive explanation.

are detailed further below

Uses "detailed further" instead of "defined", highlighting the provision of more extensive information.

are discussed in the following sections

Shifts the focus to discussing the terms rather than strictly defining them, implying a broader context.

the subsequent definitions clarify

Rephrases as a statement about the definitions themselves clarifying something, rather than introducing definitions.

the meanings are as follows

Offers a more direct way of introducing a list of definitions.

will be defined subsequently

Changes the structure to a passive voice future tense.

definitions are provided hereafter

Employs a more formal and less common adverb ("hereafter") to indicate what follows.

the terms are elucidated below

Substitutes "defined" with "elucidated", suggesting a more thorough clarification.

detailed descriptions follow

Focuses on descriptions rather than definitions, broadening the scope of information provided.

more information is presented below

Presents a broader scope, indicating additional information rather than specific definitions.

FAQs

How do I use "are defined below" in a sentence?

Use "are defined below" to introduce a list or explanation of terms that will be clarified in the following text. For example, "The key metrics, including accuracy and precision, "are defined below"."

What can I say instead of "are defined below"?

Alternatives include "are explained below", "are detailed below", or "the following definitions apply", depending on the context.

Is it redundant to say "are defined below" if the definitions are obvious?

While not grammatically incorrect, it may be unnecessary to use "are defined below" for terms that are already widely understood. Consider whether the definitions truly add value for your audience.

Where should "are defined below" be placed in a paragraph?

Typically, "are defined below" appears at the end of a sentence that introduces the terms to be defined, setting the stage for the definitions that immediately follow.