fixed point: meaning, definition, pronunciation and examples

Low
UK/ˌfɪkst ˈpɔɪnt/US/ˌfɪkst ˈpɔɪnt/

Technical/Formal

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Quick answer

What does “fixed point” mean?

A specific value, position, or state that does not change within a given system or context.

Audio

Pronunciation

Definition

Meaning and Definition

A specific value, position, or state that does not change within a given system or context; a point of stability or reference.

In mathematics, a value that is unchanged by a function or transformation. In computing, a numerical representation with a set number of digits after the decimal point. More broadly, any established, unchanging element within a process or system.

Dialectal Variation

British vs American Usage

Differences

No significant differences in meaning or usage. Spelling of related terms may differ (e.g., analyse/analyze).

Connotations

Neutral and technical in both varieties.

Frequency

Equally low-frequency in specialist contexts in both BrE and AmE.

Grammar

How to Use “fixed point” in a Sentence

The [NOUN] has a fixed point at [VALUE].[FUNCTION] maps the fixed point to itself.[SUBJECT] is a fixed point for [PROCESS].

Vocabulary

Collocations

strong
find a fixed pointcompute the fixed pointfixed point theoremfixed point arithmeticfixed point iteration
medium
serve as a fixed pointreach a fixed pointstable fixed pointfixed point of reference
weak
important fixed pointmathematical fixed pointfixed point value

Examples

Examples of “fixed point” in a Sentence

verb

British English

  • The algorithm is designed to **fixed-point** on the solution.
  • We need to **fixed-point iterate** to find the root.

American English

  • The function will **fixed-point** after several iterations.
  • The system is **fixed-pointing** on an equilibrium.

adjective

British English

  • We used a **fixed-point** representation for the financial data.
  • The **fixed-point** theorem is a key result.

American English

  • The microcontroller uses **fixed-point** arithmetic.
  • He proved a **fixed-point** property for the mapping.

Usage

Meaning in Context

Business

Rarely used, except metaphorically for a stable element in a business model.

Academic

Common in mathematics, computer science, physics, and engineering literature.

Everyday

Virtually never used in everyday conversation.

Technical

The primary domain. Has precise, formal definitions in mathematics (e.g., Brouwer fixed-point theorem) and computing (fixed-point vs. floating-point representation).

Vocabulary

Synonyms of “fixed point”

Strong

equilibrium point (in dynamics)fixed value

Weak

anchor pointbenchmarkreference point

Vocabulary

Antonyms of “fixed point”

variable pointmoving targetunstable equilibriumfloating point

Watch out

Common Mistakes When Using “fixed point”

  • Using 'fixed point' in everyday language where 'fixed location' or 'meeting point' is meant.
  • Confusing 'fixed point' (computing) with 'floating point'.

FAQ

Frequently Asked Questions

It is a two-word open compound noun, similar to 'high school' or 'coffee table'.

In computing, 'fixed point' means the decimal point is in a fixed position in the number's representation, limiting range but simplifying operations. 'Floating point' allows the decimal point to 'float', enabling a wider range of values but with more complex hardware.

Yes, but usually as a metaphor. For example, 'Amid the chaos of the merger, her leadership was a fixed point for the team.'

Often a state of equilibrium where a system does not evolve, or a specific reference point (like a temperature standard such as the freezing point of water) used for calibration.

A specific value, position, or state that does not change within a given system or context.

Fixed point is usually technical/formal in register.

Fixed point: in British English it is pronounced /ˌfɪkst ˈpɔɪnt/, and in American English it is pronounced /ˌfɪkst ˈpɔɪnt/. Tap the audio buttons above to hear it.

Learning

Memory Aids

Mnemonic

Imagine a **point** on a map that is literally nailed down (**fixed**) and cannot move, no matter what.

Conceptual Metaphor

STABILITY IS IMMOBILITY; A SYSTEM IS A SPACE (with fixed points as landmarks).

Practice

Quiz

Fill in the gap
In the Banach contraction principle, a contraction mapping on a complete metric space is guaranteed to have a unique .
Multiple Choice

In which field is the term 'fixed point' LEAST likely to be used?