a fixed element of

USAGE SUMMARY

The phrase "a fixed element of" is correct and usable in written English.
It can be used to describe something that is a permanent or unchanging part of a larger system or context. Example: "Trust is a fixed element of any successful relationship."

✓ Grammatically correct

Science

Encyclopedias

News & Media

Human-verified examples from authoritative sources

Exact Expressions

6 human-written examples

Let be a fixed element of.

Fixed Point Theory and Applications

If a is a fixed element of the function space D∞, then x = (a, x) holds when x is the fixed point of a.

SEP

Let (f_{1}) and (g_{1}) be defined by (f_{1}|_{Lambda_{alpha }}=f alpha beta)) for every (alphainGamma) and (g_{1}|_{Lambda_{alpha }}=g alphabeta)) for every (alphainGamma), where β is a fixed element of Λ.

Fixed Point Theory and Applications

Let (f_{1}) and (g_{1}) be defined by (f_{1}|_{Lambda_{alpha }}=f alpha beta)) for every (alphainLambda_{m}) and (g_{1}|_{Lambda _{alpha }}=g alphabeta)) for every (alphainLambda_{m}), where β is a fixed element of Λ.

Fixed Point Theory and Applications

Recall that a discrete loop, or, simply, a loop, is a set (M) with a globally defined product for which there exists a unit element, and such that the left and the right multiplications by a fixed element of (M) are bijections.

Bulletin of Mathematical Sciences

Theorem 3.10 Let ( X, d X ) and ( R, d R ) be asymmetric metric spaces, such that d X and d R are real-valued distance functions, y ¯ be a fixed element of R, ℱ be any free filter of ℕ and suppose that (3.10.1) each subset of R, ℱ-closed and ℱ-forward bounded with respect to y ¯, is ℱ-compact.

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

53 human-written examples

Since x n i 0 is any fixed element of { x n i }, then for any element x n i of { x n i }, we have that x n i ≤ x ∗.

Fixed Point Theory and Applications

These conclusions hold for a fixed element size of 16 pixels.

EURASIP Journal on Image and Video Processing

The Halpern iterative process generates a sequence { x n } in the following manner: x 1 ∈ C, x n + 1 = α n u + ( 1 − α n ) T x n, ∀ n ≥ 1, where x 1 is an initial and u is a fixed element in C. Strong convergence of Halpern iterative process does not depend on metric projections.

Fixed Point Theory and Applications

for all ϕ ∈ E 0. For a fixed element c ∈ I, the Razumikhin class of functions in E 0 is defined by R c = { ϕ ∈ E 0 : ∥ ϕ ∥ E 0 = ∥ ϕ ( c ) ∥ E }. (1.2).

Journal of Inequalities and Applications

for all ϕ ∈ E 0. For a fixed element c ∈ I, the Razumikhin class of mappings in E 0 is defined by R c = { ϕ ∈ E 0 : ∥ ϕ ∥ E 0 = ∥ ϕ ( c ) ∥ E }. (1.2).

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When using "a fixed element of", ensure the context clearly establishes what the element is fixed in. For instance, specify whether it's fixed within a system, a process, or a relationship.

Common error

Avoid using "a fixed element of" without clearly defining the scope or system to which the element is fixed. Ambiguity can arise if the reader doesn't understand what the element is a constant part of.

Linguistic Context

The phrase "a fixed element of" functions primarily as a modifier, specifying that something is a constant and unchanging part of a larger entity or system. As Ludwig AI points out, its grammatical correctness is well established. This usage aligns with examples from various sources.

Expression frequency: Uncommon

Frequent in

Science

60%

Encyclopedias

17%

News & Media

12%

Less common in

Formal & Business

0%

Wiki

5%

Academia

0%

Ludwig's WRAP-UP

In summary, "a fixed element of" is a grammatically correct phrase used to describe a constant or unchanging part of something. As Ludwig AI's analysis shows, its primary function is to modify and define a stable aspect within a system or context. While less frequent than some alternatives, it is particularly common in scientific and academic writing, where precision and objectivity are valued. When using this phrase, it's important to clearly establish the context to avoid ambiguity.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

an immutable component within

Emphasizes the unchanging nature of the component using "immutable", implying a more rigid and permanent aspect.

a constant feature of

Uses "constant" to highlight the unchanging quality, suitable when referring to recurring characteristics.

an unvarying aspect of

Replaces "fixed element" with "unvarying aspect", focusing on the lack of variation.

a permanent fixture in

Highlights the enduring presence of the element, suggesting it is well-established and unlikely to change.

a stable portion of

Suggests reliability and resistance to change, using "stable" to convey a sense of steadiness.

an established part of

Focuses on the element's acceptance and integration within the system, indicating it is well-recognized.

a set characteristic of

Emphasizes that the element is a defined attribute of something. "Set characteristic" suggests a clear and predetermined quality.

an inherent attribute in

Indicates the element is intrinsically part of something, suggesting it is a natural and inseparable quality.

a core ingredient of

Implies that the element is essential and fundamental, similar to a necessary component in a recipe.

a built-in aspect of

Focuses on the element being integrated from the beginning, suggesting it is an original and intended feature.

FAQs

How can I use "a fixed element of" in a sentence?

You can use "a fixed element of" to describe something constant or unchanging within a larger context. For example: "Trust is "a fixed element of" any successful relationship".

What are some alternatives to "a fixed element of"?

Alternatives include "an immutable component within", "a constant feature of", or "an unvarying aspect of", depending on the nuance you want to convey.

Is "a fixed element of" formal or informal?

"A fixed element of" leans towards formal usage, often found in academic or technical contexts. In casual conversation, you might prefer simpler alternatives like "a key part of".

What's the difference between "a fixed element of" and "an integral part of"?

While both indicate essential components, ""a fixed element of"" emphasizes constancy and immutability. "an integral part of" simply highlights necessity or essentiality without necessarily implying it does not change.