be a given set

USAGE SUMMARY

The phrase "be a given set" is correct and usable in written English.
It can be used in mathematical or logical contexts to refer to a specific set that is defined or assumed for the purpose of discussion or analysis. Example: "In this problem, let X be a given set of integers that we will analyze for patterns."

✓ Grammatically correct

Science

News & Media

Academia

Human-verified examples from authoritative sources

Exact Expressions

11 human-written examples

Let (Esubseteq W) be a given set.

Boundary Value Problems

Finally, let (Esubseteq X) be a given set.

Advances in Difference Equations

Let be a given set in ordered by or by.

Journal of Inequalities and Applications

Let X be a given set and C be a subset of X.

Fixed Point Theory and Applications

Let X be a given set and let C be a subset of X.

Fixed Point Theory and Applications

Let X be a given set and (f:Xtimes Xrightarrow mathbb{R}) be a given function.

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

49 human-written examples

Let be a given set-valued mapping.

Fixed Point Theory and Applications

Let (S: Xrightarrow2^{Y}) be a given set-valued map.

Journal of Inequalities and Applications

Let F : A × A → 2 Z be a given set-valued mapping.

Journal of Inequalities and Applications

Let F : K × K → 2 Z be a given set-valued mapping.

Journal of Inequalities and Applications

He tended to consider a given state of the universe as being a given set of premisses, so to say, of a possible inference.

SEP

Expert writing Tips

Best practice

When using "be a given set" in mathematical or logical contexts, ensure the set's properties and elements are clearly defined to avoid ambiguity.

Common error

Avoid using "be a given set" without specifying the elements or properties of the set. Always provide a clear definition to ensure the context is understood.

Linguistic Context

The phrase "be a given set" functions as a mathematical or logical declaration, introducing a specific set that is already defined or assumed for the context. Ludwig AI shows its use in various academic and scientific publications.

Expression frequency: Common

Frequent in

Science

53%

Academia

21%

News & Media

9%

Less common in

Formal & Business

6%

Wiki

5%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "be a given set" is a phrase commonly used in academic and scientific writing to introduce a set that is already defined or assumed for the context. As Ludwig AI confirms, its grammatical status is correct, and it is frequently found in formal contexts. When using this phrase, it's important to ensure clarity in the set's definition to avoid ambiguity. Alternatives such as "consider a defined set" or "assume a specified set" can be used depending on the specific nuance you want to convey. Make sure to define the set clearly to avoid vagueness.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

consider a defined set

This alternative replaces "be given" with "consider", implying active selection of the set for analysis or discussion.

assume a specified set

Using "assume" emphasizes that the set's properties are taken as true for the purpose of a specific argument or proof.

let there be a predetermined set

This alternative uses more formal language, suitable for mathematical or logical proofs.

take a known set

The term "take" suggests the set is already established and readily available for use.

presume a fixed set

"Presume" indicates that the set is believed to be established without requiring further proof or definition.

stipulate a particular set

"Stipulate" implies a formal agreement or condition where a specific set is defined for a particular purpose.

define a specific set

This option emphasizes the action of establishing the set's composition and properties.

establish a designated set

"Establish" suggests creating or identifying a set for explicit use in a process or analysis.

a set under consideration

This highlights that the set is the current focus of attention or analysis.

a set in question

Implies that the set's properties or relevance are being investigated or discussed.

FAQs

How can I use "be a given set" in a sentence?

You can use "be a given set" to introduce a set that is already defined or assumed for a particular purpose, such as in mathematical proofs or logical arguments. For example: "Let X "be a given set" of integers."

What phrases are similar to "be a given set"?

Similar phrases include "consider a defined set", "assume a specified set", or "let there be a predetermined set", which all indicate that a particular set is being established or taken as a starting point.

Is it more formal to say "be a given set" or "consider a set"?

"Be a given set" is generally more formal and is often used in academic and scientific writing, particularly in mathematical or logical contexts. "Consider a set" is slightly less formal and can be used in a broader range of contexts.

When should I use "be a given set" instead of simply defining a set?

Use "be a given set" when the set's definition is already understood or has been previously established within the context of the discussion or proof. It's suitable when you don't need to explicitly define the set's elements but rather refer to it as a pre-existing entity.