a subsequence of which

USAGE SUMMARY

The phrase "a subsequence of which" is correct and usable in written English.
It can be used when referring to a part of a sequence or series that is derived from a larger set, often in mathematical or technical contexts. Example: "The data set contains several sequences, a subsequence of which is particularly relevant to our analysis."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

33 human-written examples

Thus there is a subsequence of which converges strongly to.

Fixed Point Theory and Applications

Since is bounded, we can choose a subsequence of which converges weakly some point x.

Journal of Inequalities and Applications

Since is bounded, we can choose a subsequence of which converges weakly to some point x.

Journal of Inequalities and Applications

Since, there exist and a subsequence of, which is still denote by, such that (58).

Advances in Difference Equations

(iii) We prove that there exists a subsequence of which converges weakly to, where.  .

Fixed Point Theory and Applications

Since is bounded and is closed, there exists a subsequence of which converges weakly to, where.

Fixed Point Theory and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

27 human-written examples

This implies that for any positive integer sequence, as, there is a subsequence of for which converges uniformly on as.

Advances in Difference Equations

For given ({varphi _{k_{j}}}), there exist a continuous function φ and, maybe, a subsequence of it, which is also denoted by ({varphi_{k_{j}}}), such that (varphi_{k_{j}}rightarrowvarphi), (k_{j}rightarrow0), as (Mrightarrowinfty).

Boundary Value Problems

Suppose that (x_n=fx) for infinitely many (nin mathbb {N}), then there exists a subsequence of ({x_n}) which converges to fx and the uniqueness of the limit finish the proof.

Mathematical Sciences

For E. coli, the Shine-Dalgarno sequence was determined to be a subsequence of AGGAGGU (which is the reverse complement of the 3' end of the 16S rRNA), and the minimum AU-richness (equivalent to ribosome binding capacity) of the preceding region was arbitrarily set to 10/16.

Plosone

Indeed, suppose on the contrary that there exists a subsequence of ((u_{n})_{n}), which we label the same, for which (min u_{n}(t)>n).

Boundary Value Problems

Expert writing Tips

Best practice

When using "a subsequence of which", ensure the context clearly defines the original sequence and the criteria for selecting the subsequence.

Common error

Avoid using "a subsequence of which" when the order is not important. "Subsequence" implies maintaining the order of elements from the original sequence, while "subset" does not.

Linguistic Context

The phrase "a subsequence of which" functions as a relative clause, specifying a subset of a sequence that maintains the original order. According to Ludwig AI, it is grammatically correct and commonly used in scientific and mathematical contexts. It modifies a noun phrase by providing more information about a specific part of the sequence in question.

Expression frequency: Common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

In summary, "a subsequence of which" is a grammatically sound phrase predominantly used in scientific and mathematical writing to denote a specific part of a larger sequence, maintaining the original order of elements. As Ludwig AI confirms, its usage is correct and common within these specialized contexts. It’s important to distinguish it from terms like "subset" when the order matters. Alternative phrases such as "a portion of which" or "a segment of which" can be used depending on the context to maintain clarity. Remember to clearly define the original sequence when using the expression and to avoid redundancy by not using "subsequent" with it.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

a subset of which

Focuses on a set-based selection rather than sequential order.

a portion of which

Emphasizes a part or fraction of the original sequence.

a segment of which

Highlights a continuous section taken from the sequence.

a section of which

Indicates a distinct part or division within the sequence.

a part of which

A general term for any portion of the sequence.

a component of which

Stresses that the element belongs to the whole original sequence.

a fraction of which

Emphasizes the proportional aspect of the selected portion.

a piece of which

Suggests a smaller, possibly non-contiguous, element extracted from the sequence.

an element of which

Refers to a single item within the overall sequence.

a member of which

Highlights the inclusion of an item within the group that forms the sequence.

FAQs

How is "a subsequence of which" used in mathematical contexts?

In mathematics, "a subsequence of which" refers to a sequence derived from another sequence by selecting some of its elements, maintaining their original order. It's often used in proofs related to convergence and limits.

What does "a segment of which" mean?

A segment of which, similar to "a subsequence of which", refers to a continuous portion taken directly from the original sequence, maintaining order and adjacency.

Is it correct to say "a subsequent sequence of which"?

The phrase "a subsequent sequence of which" is redundant. Using "a subsequence of which" already implies that the derived sequence follows from the original one.

What are some alternatives to using "a subsequence of which"?

Depending on the context, you can use alternatives such as "a subset of it", "a portion of the sequence", or "a part of it" for better clarity or conciseness.