is defined to be

USAGE SUMMARY

The phrase "is defined to be" is a valid and usable phrase in written English.
It is typically used to introduce a definition or to explain the meaning of a word or phrase. For example, "Decorum is defined to be the practice of behaving and speaking in a respectful manner."

✓ Grammatically correct

Science

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

A topological property is defined to be a property that is preserved under a homeomorphism.

Encyclopedia Britannica

Time is defined to be t.

Robotics and Biomimetics

For every, the spectral radius of is defined to be.

Journal of Inequalities and Applications

The weight error is defined to be (11).

EURASIP Journal on Advances in Signal Processing

The norm of an matrix is defined to be (2.7).

Advances in Difference Equations

The Pták function on -algebra is defined to be, where.

Journal of Inequalities and Applications

The spectral radius of is defined to be.

Fixed Point Theory and Applications

(assuming that the x axis is defined to be the direction of their relative motion).

SEP

Thus z−1 is defined to be that x such that z × x = 1.

SEP

A procedure that attains this lower bound is defined to be asymptotically best.

Journal of Statistical Planning and Inference

A consistent highway geometric design is defined to be one that conforms to the driver's expectations.

Journal of Traffic and Transportation Engineering (English Edition)

Expert writing Tips

Best practice

When using "is defined to be", ensure that the definition is clear, concise, and appropriate for your target audience. Avoid circular definitions or jargon that may confuse readers.

Common error

Avoid defining terms with unnecessarily complicated language. Ensure that the definition is accessible to the intended audience, maintaining clarity and precision.

Linguistic Context

The phrase "is defined to be" serves as a defining verb phrase. It explicitly introduces the meaning or definition of a term, concept, or variable. As Ludwig AI indicates, the phrase is very common in academic and scientific writing.

Expression frequency: Very common

Frequent in

Science

75%

Encyclopedias

15%

Formal & Business

5%

Less common in

News & Media

2%

Wiki

2%

Reference

1%

Ludwig's WRAP-UP

The phrase "is defined to be" is a standard and highly functional linguistic tool, predominantly employed in academic, scientific, and formal writing. Ludwig AI confirms its widespread usage to introduce precise definitions, ensuring clarity and preventing ambiguity. While grammatically sound and widely accepted, it's crucial to tailor the complexity of the definition to the target audience. Alternatives such as "is understood as" or "is considered to be" may be appropriate in less formal contexts. The key is to prioritize clarity and precision when defining terms, adhering to the intended communication style. Using synonyms to change vocabulary enriches text but does not alter the underlying function.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

is understood as

Focuses on comprehension or interpretation rather than a strict definition.

is considered to be

Highlights a generally accepted view or classification.

is known as

Emphasizes common knowledge or recognition.

is characterized as

Stresses the distinctive features or qualities of something.

is interpreted as

Implies a subjective understanding or analysis.

is designated as

Suggests a formal assignment or labeling.

is termed as

Emphasizes the use of a specific term or nomenclature.

is identified as

Focuses on recognition or classification within a system.

is stipulated to be

Highlights a condition or requirement that must be met.

amounts to

Indicates an equivalence or resultant value.

FAQs

How can I use "is defined to be" in a sentence?

Use "is defined to be" to clearly state the meaning of a term or concept. For example, "A homeomorphism "is defined to be" a continuous mapping between topological spaces that has a continuous inverse."

What are some alternatives to "is defined to be"?

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

Is it redundant to say "is defined as being" instead of "is defined to be"?

While "is defined as being" isn't grammatically incorrect, it can often be more concise and clear to simply use ""is defined to be"". The "being" can be redundant in many cases.

What is the difference between "is defined to be" and "means"?

"Is defined to be" is generally used for formal definitions, especially in technical or academic contexts. "Means" is a more general term for indicating equivalence or conveying the meaning of something.