defined as follows

USAGE SUMMARY

"defined as follows" is a correct and usable phrase in written English.
You can use it when you are introducing or explaining a definition or description. For example: The term "student" is defined as follows: a person enrolled in an educational institution.

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

59 human-written examples

The problem is defined as follows.

Theoretical Computer Science

The apparent quantum yield (ΦH2) is defined as follows.

Nature

Let \(g : B → A\) be defined as follows.

Cornell University

This score is defined as follows (view slide).

Harvard University

More precisely, finiteness is defined as follows.

SEP

That notion is defined as follows.

SEP

These notions are defined as follows.

SEP

defined as follows.

Advances in Difference Equations

It was defined as follows.

Journal of Inequalities and Applications

These are defined as follows.

Bulletin of Mathematical Sciences

SNR is defined as follows.

EURASIP Journal on Advances in Signal Processing

Expert writing Tips

Best practice

Use "defined as follows" when you are about to provide a formal or technical definition. It signals to the reader that a specific and precise meaning will be given.

Common error

Avoid using "defined as follows" in casual conversation or informal writing. Opt for simpler alternatives like "meaning" or "basically" to maintain a natural tone.

Linguistic Context

The phrase "defined as follows" serves as an introductory signal, preparing the reader for a subsequent definition or explanation. According to Ludwig, it is grammatically correct and usable in written English. Examples in the provided data showcase its frequent use in scientific and academic contexts.

Expression frequency: Very common

Frequent in

Science

89%

Academia

10%

Formal & Business

1%

Less common in

News & Media

0%

Encyclopedias

0%

Reference

0%

Ludwig's WRAP-UP

In summary, "defined as follows" is a grammatically correct and highly functional phrase used to introduce precise definitions, particularly in formal and scientific writing. Ludwig AI confirms its usability. Its frequency and prevalence in academic and scientific sources underscore its importance in contexts requiring clarity and accuracy. While effective in these settings, it's best to avoid it in informal communication, where simpler alternatives may be more appropriate.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

described as follows

A straightforward alternative that emphasizes the act of providing a description.

characterised as follows

Focuses on identifying the key traits or features of something, emphasizing its distinct qualities.

ascertained as follows

Focuses on the process of finding something out, suggesting a more investigative tone.

determined as follows

Highlights the act of reaching a conclusion or decision about something, implying a more definitive quality.

interpreted as follows

Emphasizes a particular understanding or reading of something, suggesting a subjective element.

delineated as follows

Implies drawing a clear boundary or outline, suggesting precision and detail.

categorized as follows

Highlights the act of classifying something into specific groups, emphasizing organization and structure.

classified as follows

Similar to categorized, but can also imply a hierarchical arrangement.

conceptualized as follows

Emphasizes the mental construction or idea behind something, highlighting theoretical aspects.

designated as follows

Highlights a specific naming or appointment, suggesting an official or formal assignment.

FAQs

How to use "defined as follows" in a sentence?

The phrase "defined as follows" is typically used to introduce a formal definition. For example, "The term 'algorithm' is defined as follows: a step-by-step procedure for solving a problem."

What can I say instead of "defined as follows"?

You can use alternatives like "described as follows", "characterized as follows", or "can be defined as" depending on the context.

Which is correct, "defined as follows" or "defined as following"?

"Defined as follows" is the correct and more common phrase. "Defined as following" is grammatically incorrect in this context.

What's the difference between "defined as follows" and "as defined as following"?

"Defined as follows" introduces a definition immediately. "As defined as following" is grammatically incorrect. The phrase "as defined by" is used to attribute a definition to a specific source.