is formally defined as

USAGE SUMMARY

The phrase "is formally defined as" is correct and usable in written English.
It can be used when introducing a precise definition or explanation of a term or concept in a formal context. Example: "In mathematics, a function is formally defined as a relation that assigns exactly one output for each input."

✓ Grammatically correct

Science

News & Media

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

The NE of the game is formally defined as follows (Krause et al. 2006): In a n-person game, the strategy profile p ∗ = ( p 1 ∗, …, p n ∗ ) is a NE if for all i ∈ 1, …, n we have: U i ( p 1 ∗, …, p n ∗ ) ≥ U i p 1 ∗, …, p i - 1 ∗, p i, p i + 1 ∗, …, p n ∗ (6).

Journal of Industrial Engineering International

To be sure, corruption is formally defined as the misuse of public office for private gain – not lying during a political campaign.

The Guardian - Lifestyle

Economic nationalism is formally defined as encompassing domestic control of the economy, protectionist policies such as tariffs and opposition to trade and immigration.

The New York Times

Mechatronics is formally defined as the synergistic combination of precision mechanical engineering, electronic control, and systems thinking in the design of products and manufacturing processes.

Mechatronics Principles and Applications

IRE is formally defined as the line integral of a special function (the infinitesimal road effect) along the curves that model the roads, whereas AVIRE is the quotient of IRE by the length of the roads.

Ecological Modelling

FEMALE SEXUAL AROUSAL DISORDER What it is Formally defined as the inability to attain or maintain sufficient sexual excitement, its symptoms include lack of libido, decreased sensation and reduced arousal and excitement.

Independent

Mobility is formally defined as the value of the drift velocity per unit of electric field strength; thus, the faster the particle moves at a given electric field strength, the larger the mobility.

Encyclopedia Britannica

The thermodynamic least work of dehumidification and cooling is formally defined as a thermodynamic benchmark, while VCS performance is chosen as the industry benchmark against which other technologies, namely desiccant-based cooling system (DCS) and membrane-based cooling system (MCS), are compared.

Applied Energy

It is formally defined as follows.

Complex Adaptive Systems Modeling

The BLE is formally defined as follows.

EURASIP Journal on Wireless Communications and Networking

A network group is formally defined as follows.

EURASIP Journal on Wireless Communications and Networking

Expert writing Tips

Best practice

When using "is formally defined as", ensure that the definition you provide is accurate, specific, and appropriate for the context. Avoid vague or ambiguous language.

Common error

Avoid following a formal definition introduced by "is formally defined as" with informal explanations or examples that undermine the precision of the definition. Maintain a consistent level of formality.

Linguistic Context

The phrase "is formally defined as" serves as a definitional verb phrase. It explicitly introduces a rigorous definition of a term or concept. The examples Ludwig provides underscore this function, demonstrating its use across varied academic and technical fields.

Expression frequency: Very common

Frequent in

Science

76%

News & Media

12%

Encyclopedias

2%

Less common in

Formal & Business

1%

Wiki

0%

Reference

0%

Ludwig's WRAP-UP

In summary, the phrase "is formally defined as" is a powerful tool for introducing precise definitions, predominantly used in formal and scientific writing. According to Ludwig, it is used in academic papers, scientific articles, and technical documentation, where precision and accuracy are paramount. It is grammatically sound and very common, serving to eliminate ambiguity by providing clear and agreed-upon meanings for specific terms. When employing this phrase, maintain accuracy and consistency in the level of formality to ensure effective communication.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

is officially defined as

Replaces "formally" with "officially", suggesting an authorized or recognized definition.

is technically defined as

Substitutes "formally" with "technically", implying a definition specific to a technical field or context.

is precisely defined as

Uses "precisely" instead of "formally", emphasizing the accuracy and exactness of the definition.

is stipulated as

Replaces "defined" with "stipulated", indicating that the definition is set forth as a condition or requirement.

is designated as

Uses "designated" instead of "defined", suggesting an assignment or naming of a specific quality or role.

is characterized as

Shifts the focus to describing the characteristics of something, rather than giving a strict definition.

can be defined as

Introduces a possibility or allowance in the definition, making it less absolute.

is understood to be

Emphasizes a general understanding or consensus about the meaning of something.

is considered to be

Highlights a particular viewpoint or perspective in defining something.

is known as

Suggests a common or recognized name or label for something, rather than a formal definition.

FAQs

How can I use "is formally defined as" in a sentence?

Use "is formally defined as" to introduce a precise, technical, or official definition of a term. For example, "A black hole "is formally defined as" a region of spacetime with such strong gravitational effects that nothing, not even particles and electromagnetic radiation such as light, can escape from inside it."

What are some alternatives to "is formally defined as"?

You can use alternatives like "is officially defined as", "is technically defined as", or "is precisely defined as" depending on the context and the level of formality you want to convey.

Is it appropriate to use "is formally defined as" in informal writing?

While "is formally defined as" is generally used in formal contexts, it can be used in informal writing if you need to introduce a technical term or concept that requires a precise definition. However, consider whether a simpler, less formal phrasing would be more appropriate for your audience.

What's the difference between "is formally defined as" and "is generally known as"?

"Is formally defined as" introduces a specific, often technical, definition, while "is generally known as" refers to a common or popular understanding, which may not be precise or universally accepted.