be a given sequence

USAGE SUMMARY

The phrase "be a given sequence" is correct and usable in written English.
It can be used in mathematical or programming contexts to refer to a specific sequence that is defined or assumed for a particular discussion or analysis. Example: "Let x be a given sequence of numbers that converges to a limit."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

8 human-written examples

Let be a given sequence in such that (7.12).

Journal of Inequalities and Applications

Let be a given sequence of positive numbers and a positive number such that there exists a number satisfying (1.4).

Advances in Difference Equations

Let { λ n } be a given sequence in ( 0, 1 ) such that ∑ n = 1 ∞ λ n = 1, let { v n } be a bounded sequence in X, and let v 0 be an arbitrary point in X.

Fixed Point Theory and Applications

Let ( μ m n be a given sequence and μ = ( μ m n i j be a diagonal matrix whose only non-zero entries are μ m n = μ m n m n.

Journal of Inequalities and Applications

Let (t=(t_{k})) be a given sequence of nonnegative numbers such that (liminf_{k} t_{k}>0) and (T_{m}=sum_{k=0}^{m-1}t_{k}neq0) for all (mgeq1).

Journal of Inequalities and Applications

Let (t=(t_{k})_{kinmathbb {N}}) be a given sequence of nonnegative numbers such that (liminf_{k} t_{k}>0) and (T_{m}=sum_{k=0}^{m-1}t_{k}neq0) for all (mgeq1).

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

52 human-written examples

Recall (see [52, 53]) that if is a given sequence in, is defined recurrently by and for.

Journal of Inequalities and Applications

Now, if is a -norm and is a given sequence of numbers in, we define a sequence recursively by and for all. is defined as.

Journal of Inequalities and Applications

Recall (see [46, 49]) that if is a -norm and is a given sequence of numbers in, is defined recurrently by (23). is defined as.

Fixed Point Theory and Applications

Recall (see [42, 43]) that if is a -norm and is a given sequence of numbers in, is defined recurrently by and for.

Journal of Inequalities and Applications

Recall (see [29, 30]) that, if is a -norm and is a given sequence of numbers in, then is defined recurrently by (1.7).

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When using "be a given sequence", ensure the context clearly defines or implies how the sequence is determined. This avoids ambiguity and clarifies the subsequent analysis or operations involving the sequence.

Common error

Avoid using "be a given sequence" without providing sufficient information about the sequence's origin or properties. For instance, specify if it's a numerical sequence, a DNA sequence, or a sequence of operations to ensure readers understand its nature.

Linguistic Context

The phrase "be a given sequence" primarily functions as a mathematical or logical construct, used to introduce a sequence that is assumed or pre-defined within a specific context. Ludwig AI confirms that this phrase is correctly used to set up conditions or assumptions, as demonstrated in various examples.

Expression frequency: Common

Frequent in

Science

85%

Academia

10%

Formal & Business

5%

Less common in

News & Media

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "be a given sequence" is a common and grammatically correct expression, predominantly used in scientific and mathematical contexts to introduce a pre-defined sequence. As Ludwig AI indicates, it's crucial to provide sufficient context regarding the sequence's origin and properties to avoid ambiguity. Related phrases include "consider a specified sequence" and "assume a defined sequence". When using this phrase, ensure clarity in defining the sequence to maintain precision in your writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

consider a specified sequence

Replaces "be" with "consider", making the phrase more active and direct.

assume a defined sequence

Uses "assume" instead of "be", highlighting the hypothetical nature of the sequence.

let's define a sequence

Emphasizes the act of defining the sequence, suitable for introductory contexts.

suppose a known sequence

Highlights that the sequence is already known or established.

a predetermined sequence

Focuses on the sequence being decided in advance.

a pre-established sequence

Similar to "predetermined", but emphasizes the sequence's long-standing existence.

a fixed sequence

Implies that the sequence is unchangeable and constant.

a set sequence

Similar to "fixed", suggesting a defined and unvarying order.

an established sequence

Highlights that the sequence is recognized and accepted.

a designated sequence

Indicates that the sequence has been specifically chosen or assigned.

FAQs

How do I use "be a given sequence" in a sentence?

You can use "be a given sequence" to introduce a sequence that is already defined or assumed for a particular purpose. For example, "Let x "be a given sequence" of numbers that converges to a limit".

What can I say instead of "be a given sequence"?

You can use alternatives like "consider a specified sequence", "assume a defined sequence", or "let's define a sequence" depending on the context.

Which is correct, "be a given sequence" or "is a given sequence"?

"Be a given sequence" is generally used in mathematical and programming contexts to define a condition or assumption. "Is a given sequence" is used to state a fact. The correct usage depends on the context.

What's the difference between "be a given sequence" and "a predetermined sequence"?

"Be a given sequence" implies that the sequence is pre-existing or defined elsewhere, while "a predetermined sequence" emphasizes that the sequence was decided in advance.