under this relation

USAGE SUMMARY

The phrase "under this relation" is correct and usable in written English.
It can be used in contexts where you are discussing a specific relationship or connection between concepts, entities, or variables. Example: "Under this relation, we can deduce that the two variables are directly proportional to each other."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

Under this relation the space of possible mathematical systems forms an intricate hierarchy of increasingly strong systems.

SEP

This is an equivalence relation on the hyperreal line: for each hyperreal a we write μ(a) for the equivalence class of a under this relation and call it the monad of a.

SEP

It is also easy to see that the classes \ \textbf{P}, \textbf{NP}, \textbf{PSPACE},\textbf{EXP}, \textbf{NEXP}\) and \ \textbf{EXPSPACE}\) are closed under this relation.[16] A problem \(Y\) is said to be hard for a class \ \textbf{C}\) if \(X \leq_P Y\) for all \(X \in \textbf{C}\).

SEP

Human-verified similar examples from authoritative sources

Similar Expressions

57 human-written examples

If so, does blueness "fall under" this universal in the same sense as the sense in which a copy of Philosophical Studies falls under blueness?) Now what can we say about this relation, this "falling under"?

SEP

At the same time, upper approximation and lower approximation are defined under this improved relation.

Water Science and Engineering

1. Probably the best all-purpose understanding of what logics are would take them as equivalence classes of proof systems under the relation of having mutually interderivable rules, though even this ignores issues about translational equivalence across differing languages.

SEP

One very general way to investigate the space of possible mathematical systems is under the relation of interpretability.

SEP

The interpretability hierarchy is the collection of all theories (satisfying our three simplifying assumptions) ordered under the relation ≤.

SEP

A binary relation (mathcal{R}) is called complete if every elements are comparable under that relation (i.e., ([x,y]in mathcal{R}) (forall x,yin X)).

Fixed Point Theory and Applications

If she does so, then she indirectly ascribes the property of being hungry to Bill, under the relation of being a man uniquely seen.

SEP

In other words, [ j] is the equivalence class of vertex j under the relation of strong connectivity, as defined above.

BMC Biology

Expert writing Tips

Best practice

When using "under this relation", ensure the relationship being referenced is clearly defined and understood by the reader. This avoids ambiguity and strengthens the logical flow of your writing.

Common error

Avoid using "under this relation" in casual or informal writing. It can sound overly formal or stilted. Opt for simpler alternatives like "in this case" or "because of this" in less formal settings.

Linguistic Context

The phrase "under this relation" functions as a prepositional phrase that modifies a verb or clause. It introduces a condition or framework within which something else occurs. As Ludwig AI explains, the phrase is grammatically correct.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Ludwig's WRAP-UP

In summary, the phrase "under this relation" is grammatically correct but relatively rare in everyday usage. According to Ludwig AI, the phrase is usable in written English, particularly in formal, academic, and scientific contexts. It serves to specify the conditions or context dictated by a defined relationship. While it's valuable for precise communication in specialized fields, it should be used sparingly in informal writing to avoid sounding overly formal. Consider alternatives like "in this context" or "given this relationship" to better suit the situation.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

within this connection

Replaces "relation" with "connection", emphasizing a link or association.

governed by this relationship

Replaces "under" with "governed by", highlighting a controlling influence.

subject to this association

Uses "subject to" instead of "under", conveying a dependency.

according to this link

Replaces "under" with "according to" which conveys being in agreement or conformity with the given relationship

in the context of this link

Uses "in the context of" to introduce the framework of the relationship

with respect to this connection

Replaces "under" with "with respect to", indicating a specific point of view or consideration.

in light of this association

Emphasizes understanding something based on the specified relationship.

based on this link

Highlights that something relies on the particular relationship.

in view of this relationship

Similar to "in light of", but emphasizes considering the relationship.

considering this link

Focuses on the action of taking the relationship into account.

FAQs

How can I use "under this relation" in a sentence?

Use "under this relation" to specify conditions or consequences dictated by a defined relationship. For example, "Under this relation, increasing variable A will decrease variable B."

What are some alternatives to "under this relation"?

Consider alternatives like "in this context", "with respect to this", or "given this relationship", depending on the specific nuance you want to convey. See also: "within this connection".

Is "under this relation" suitable for informal writing?

Generally, no. "Under this relation" is more appropriate for formal or academic writing. In informal contexts, simpler phrases are preferable. Use instead: "in this case" or "because of this".

What does "under this relation" exactly mean?

"Under this relation" means operating within the framework or conditions established by a specific relationship between elements or concepts. It indicates that certain rules or consequences apply due to this relationship.