fixed point

USAGE SUMMARY

"fixed point" is a correct and usable phrase in written English.
You can use it to refer to a point in a process, discussion, or argument that is determined and unchangeable. For example, "We had a disagreement about the project, but we agreed to the fixed point that it should be finished by the end of the month."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

It is very natural to extend the definition of two-dimensional fixed point (coupled fixed point), three-dimensional fixed point (tripled fixed point) and so on to multidimensional fixed point (n-tuple fixed point) (see, e.g., [9 17]).

Journal of Inequalities and Applications

The coupled fixed point extends to a tripled fixed point.

Fixed Point Theory and Applications

It is restless and not graspable from any fixed point.

The Guardian - Arts

Hence, has fixed point and fixed point.

Advances in Difference Equations

Therefore, has fixed point and fixed point.

Advances in Difference Equations

Generalized fixed point theorems.

Advances in Difference Equations

(Brouwer fixed point theorem).

Fixed Point Theory and Applications

(Banach fixed point theorem).

Advances in Difference Equations

(Browder fixed point theorem).

Boundary Value Problems

(Kakutani fixed point theorem).

Fixed Point Theory and Applications

By Schauder fixed point theorem, has a fixed point.

Fixed Point Theory and Applications

Expert writing Tips

Best practice

When using "fixed point" in technical writing, ensure you clearly define the context, whether you're referring to a mathematical concept, a stable reference, or a determined stage in a project.

Common error

Avoid using "fixed point" when you mean "focal point". "Fixed point" refers to something stable and unchanging, while "focal point" refers to the center of interest or attention. Using the wrong term can confuse your readers.

Linguistic Context

The phrase "fixed point" primarily functions as a noun, often describing a specific, invariant value or location within a system or process. Ludwig examples show its use in mathematical contexts to describe a point unchanged by a function, and in general contexts to describe an unmoving physical or abstract location.

Expression frequency: Very common

Frequent in

Science

70%

News & Media

20%

Formal & Business

5%

Less common in

Wiki

3%

Encyclopedias

1%

Reference

1%

Ludwig's WRAP-UP

In summary, "fixed point" is a versatile noun phrase with a well-defined meaning across various domains. It denotes something stable and unchanging. Ludwig AI confirms it is grammatically correct and frequently used. While its primary function is to indicate stability, the context determines its specific application, ranging from mathematical invariants to unchanging references. When using "fixed point", it's important to distinguish it from "focal point" and ensure clarity regarding the context to avoid confusion. The phrase is most commonly found in scientific and news-related sources.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

invariant point

This mathematically inclined phrase expresses the point remains unaltered under a transformation.

unchanging reference

This alternative focuses on the idea of something that does not change, highlighting its role as a reference.

stable element

This phrase emphasizes the stability and enduring nature of the element in question.

constant factor

This option highlights the unchanging nature of the factor within a given context.

reference point

This suggests a point used for comparison or orientation that remains consistent.

consistent variable

Emphasizes the consistent, unchanging nature of the variable.

immobile position

This highlights the lack of movement or change in the position.

stationary position

Similar to 'immobile position', it focuses on the lack of movement.

set parameter

This option suggests a parameter that has been predetermined and is not subject to change.

established benchmark

This conveys the idea of a standard that remains constant over time, used for evaluation.

FAQs

How is "fixed point" used in mathematics?

In mathematics, a "fixed point" refers to a value that remains unchanged when a function is applied to it. For example, if f(x) = x, then x is a "fixed point" of the function f.

What are some alternatives to "fixed point" when referring to a stable reference?

When referring to a stable reference, you can use alternatives such as "stable element", "unchanging reference", or "reference point", depending on the context.

Is "fixed point" the same as "focal point"?

No, "fixed point" and "focal point" have different meanings. "Fixed point" refers to something stable and unchanging, whereas "focal point" refers to the center of attention or interest.

Can "fixed point" be used in contexts other than mathematics?

Yes, "fixed point" can be used in various contexts. It can refer to a stable point in a process, a determined position in a debate, or any unchanging element in a system.