equivalent class of

USAGE SUMMARY

The phrase "equivalent class of" is correct and usable in written English.
It is typically used in mathematical or theoretical contexts to refer to a set of items that share a common property or characteristic. Example: "In set theory, we often discuss the equivalent class of rational numbers that can be expressed as fractions."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

For a common suffix with its length of, an equivalent class of hosts is defined as, where denotes the host identifiers.

EURASIP Journal on Wireless Communications and Networking

Let us fix an ordering of the vertex set V. Then the notation 〈σ〉 means the oriented simplex which belongs to the equivalent class of a natural ordering.

Pacific Journal of Mathematics for Industry

Therefore, D defines an equivalent relation on (mathbb{R}times Xtimes X), where the equivalent class of ((t,a,b)) is [toverrightarrow{ab}] = bigl{ soverrightarrow{uv} : tlangle overrightarrow{ab},overrightarrow{xy}rangle= slangleoverrightarrow {uv}, overrightarrow{xy}rangle, forall x, y in X bigr}.

Fixed Point Theory and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

57 human-written examples

We use the marketing classification of the retail company to aggregate equivalent classes of products.

EPJ Data Science

The result of meta analysis is represented as the Hasse Diagram structure of meta relations by classifying equivalent classes of fuzzy relational structures.

Fuzzy Sets and Systems

Notice that we identify functions which are equivalent, i.e., we should say that the elements of (L^{infty}[0,1]) are not functions both, rather equivalent classes of functions.

Fixed Point Theory and Applications

Theorem 2.9 infers that once | N | = max { | N j | : j ∈ Λ } is fixed, there are finitely many equivalent classes of templates and z so that the basic sets of admissible local patterns B ( T, z ) are constrained.

Boundary Value Problems

Hence, the idea of quotients and equivalent classes of (beta_{2}) and the preceding equation suggest to have ( F_{alpha }vartheta_{n} ) / ( F_{alpha } delta_{n} ) = ( F_{alpha }theta_{n} ) / ( F_{alpha }varepsilon_{n} ) quad ( m,nin N ).

Advances in Difference Equations

Ignoring this knowledge may result in a Bayesian network that captures the statistical relationships between the states of phosphoproteins perfectly but does not make any biological sense--a phenomenon referred to as equivalent classes of Bayesian networks in the machine learning field [ 30, 31].

BMC Systems Biology

While this does not mean that all genes are uniformly expressed in the two seasonal lots, it does suggest that functionally equivalent classes of liver genes are similarly regulated during times of varying photoperiod, at least within the experimental families we surveyed.

BMC Genomics

Formulating criterions for producing equivalent (equivalence classes of) score functions turns out to be most straightforwardly achieved using the general score function definition (3).

Bioinformatics and Biology Insights

Expert writing Tips

Best practice

When using "equivalent class of", ensure the context clearly defines the equivalence relation being used. This provides clarity and avoids ambiguity in technical writing.

Common error

Avoid using "equivalent class of" when you simply mean 'similar' or 'related'. The phrase specifically refers to a set of items that are considered identical under a defined equivalence relation, not just generally alike.

Linguistic Context

The phrase "equivalent class of" functions as a noun phrase that identifies a set of elements considered identical under a defined equivalence relation. As Ludwig AI confirms, its usage is precise and generally correct.

Expression frequency: Rare

Frequent in

Science

100%

News & Media

0%

Formal & Business

0%

Less common in

News & Media

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Formal & Business

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Science

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Ludwig's WRAP-UP

In summary, "equivalent class of" is a grammatically sound phrase primarily used in technical contexts, especially within science and mathematics, to denote a set of elements sharing a specific equivalence. While Ludwig AI confirms its validity, its frequency is relatively rare. It is crucial to ensure the equivalence relation is clearly defined to avoid ambiguity. In non-technical settings, consider using simpler alternatives like "group of similar items" or "category of comparable objects". Be mindful of the precise meaning and avoid using the phrase loosely to simply mean 'similar' or 'related'.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

equivalence relation

Focuses on the relationship that defines the classes, not the classes themselves.

set of equivalents

Emphasizes the collection aspect rather than the formal classification.

group of similar items

Uses more general language, suitable for less technical contexts.

category of comparable objects

Highlights comparability as the basis for categorization.

collection of analogous elements

Focuses on the analogous nature of elements within the collection.

family of related structures

Emphasizes the structural relationship between the members.

cluster of similar instances

Highlights the clustering aspect based on similarity.

classification of similar entities

Focuses on the act of classifying entities based on similarity.

aggregation of conforming items

Emphasizes that the items conform to a particular standard or pattern.

compartment of kindred objects

Uses more metaphorical language to describe the grouped objects.

FAQs

How is "equivalent class of" used in mathematics?

In mathematics, "equivalent class of" refers to a set of elements that are considered equal under a specific equivalence relation. It's a fundamental concept in set theory and algebra.

What's a simpler way to say "equivalent class of" in non-technical contexts?

In less formal contexts, you can use phrases like "group of similar items" or "category of comparable objects" to convey a similar meaning without the technical jargon.

Is there a difference between "equivalent class of" and "equivalence class of"?

No, "equivalent class of" and "equivalence class of" mean the same thing and can be used interchangeably. The latter is slightly more common in mathematical literature.

In what fields is the term "equivalent class of" commonly used?

The term "equivalent class of" is frequently used in fields like mathematics, computer science, and logic, where precise categorization based on defined relationships is essential.