we denote by

USAGE SUMMARY

"We denote by" is correct and usable in written English.
You can use it when introducing a definition or explanation of a term. For example: We denote by X the vector of all possible outcomes.

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

We denote by L2a μ,H) the equivalence classes w.r.t.

Journal of Functional Analysis

We denote by and the largest eigenvalue and the corresponding eigenvector of, respectively.

Nature

Finally, we denote by.

Journal of Inequalities and Applications

with We denote by.

Advances in Difference Equations

and we denote by.

Journal of Inequalities and Applications

We denote by either or.

Journal of Inequalities and Applications

If we denote by (3.5).

Boundary Value Problems

If for we denote by.

Fixed Point Theory and Applications

If then we denote by.

Journal of Inequalities and Applications

For simplicity, we denote by.

Journal of Inequalities and Applications

We denote by its eigenvalues.

Advances in Difference Equations

Expert writing Tips

Best practice

When using "we denote by", ensure the symbol or term being defined is clearly introduced and consistently used throughout the document.

Common error

Avoid using multiple notations for the same concept after introducing it with "we denote by". Inconsistency can lead to confusion and errors.

Linguistic Context

The phrase "we denote by" functions as an introductory phrase used to establish a specific notation or symbol for a particular concept or variable. It is prevalent in technical and academic writing, as confirmed by Ludwig AI, where clarity and precision are paramount.

Expression frequency: Very common

Frequent in

Science

90%

Formal & Business

5%

News & Media

3%

Less common in

Encyclopedias

1%

Wiki

0.5%

Social Media

0.5%

Ludwig's WRAP-UP

In summary, "we denote by" is a frequent and correct introductory phrase primarily used in formal and scientific writing to define a term. As confirmed by Ludwig AI, it serves the function of establishing clear and precise notation. While the phrase itself is grammatically sound, ensure consistent usage of defined terms throughout your document to maintain clarity. Although predominantly seen in scientific contexts, it can appear in formal business communication as well. Use simpler alternatives like "we represent by" or "we define as" if aiming for slight variations in phrasing. Remember that, although versatile, its formality may not be the best choice for casual settings.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

let us denote by

Adds a slightly more conversational tone by using "let us".

we represent by

Uses "represent" instead of "denote", implying a visual association rather than a strict definition.

we designate by

Similar to "denote" but can imply a more official or formal assignment.

is denoted by

Uses the passive voice, shifting the emphasis to the term being defined.

we symbolize by

Emphasizes the use of a symbol to stand for something, altering the focus slightly.

we define as

Highlights the act of defining, rather than simply assigning a notation.

we term as

Highlights the act of naming something a specific term.

we indicate with

Focuses on indication using a particular symbol or notation.

we label as

Implies a labeling or categorization, slightly changing the meaning.

we identify with

Suggests that a term is being linked or associated with something else.

FAQs

How is "we denote by" used in a mathematical context?

In mathematics, "we denote by" is used to introduce a symbol or notation that will represent a specific quantity, variable, or function. For example, "We denote by f(x) the derivative of the function f."

What are some alternatives to "we denote by" in academic writing?

Alternatives include "we represent by", "we define as", or "is denoted by". The choice depends on the specific nuance you want to convey.

Is it appropriate to use "we denote by" in informal writing?

While grammatically correct, "we denote by" is generally more suited for formal or technical writing. In informal contexts, simpler phrases like "let's call it" or "we'll use" might be more appropriate.

What's the difference between "we denote by" and "we define as"?

"We denote by" is primarily used to introduce a specific symbol or notation. "We define as" is broader and used to provide a full definition of a term or concept. For instance, "We denote by π the ratio of a circle's circumference to its diameter", versus "We define a function as a relation between a set of inputs and a set of permissible outputs".