strictly decreasing function: meaning, definition, pronunciation and examples
RareTechnical / Academic (primarily Mathematics)
Quick answer
What does “strictly decreasing function” mean?
A mathematical function where, as the input value increases, the output value always decreases (the inequality is strict: f(x₁) > f(x₂) for all x₁ < x₂).
Audio
Pronunciation
Definition
Meaning and Definition
A mathematical function where, as the input value increases, the output value always decreases (the inequality is strict: f(x₁) > f(x₂) for all x₁ < x₂).
A term used in mathematics, economics, and data analysis to describe a relationship where one variable consistently and necessarily goes down as another goes up. The 'strictly' indicates that the value never stays the same; it always falls.
Dialectal Variation
British vs American Usage
Differences
No difference in meaning. Pronunciation of 'function' (/ˈfʌŋk.ʃən/ vs. /ˈfʌŋk.ʃn̩/) may vary slightly, but the phrase is identical in writing and technical application.
Connotations
Purely technical, with identical connotations in both varieties.
Frequency
Used exclusively in technical/academic contexts with equal frequency in UK and US mathematical discourse.
Grammar
How to Use “strictly decreasing function” in a Sentence
[Function] is strictly decreasing on [interval]Prove that [function] is strictly decreasingA strictly decreasing function [does something]Vocabulary
Collocations
Examples
Examples of “strictly decreasing function” in a Sentence
verb
British English
- The proof aims to show the function strictly decreases across the entire interval.
- We need the curve to be strictly decreasing for the model to hold.
American English
- The algorithm requires the value to strictly decrease with each iteration.
- The data strictly decreases, confirming our hypothesis.
adverb
British English
- The values changed strictly decreasingly, which was unexpected.
American English
- The function behaves strictly decreasingly after the critical point.
adjective
British English
- We are studying strictly decreasing sequences in analysis.
- The strictly decreasing nature of the graph was evident.
American English
- A strictly decreasing trend was observed in the experiment.
- He identified a strictly decreasing pattern in the logs.
Usage
Meaning in Context
Business
Rarely used directly. Might appear in advanced economic modeling to describe demand curves under certain conditions.
Academic
Primary domain. Core concept in calculus, real analysis, and optimization.
Everyday
Virtually never used.
Technical
Standard term in mathematics, statistics, computer science (algorithm analysis), and engineering.
Vocabulary
Synonyms of “strictly decreasing function”
Neutral
Weak
Vocabulary
Antonyms of “strictly decreasing function”
Watch out
Common Mistakes When Using “strictly decreasing function”
- Omitting 'strictly' when the strict condition is intended.
- Confusing 'strictly decreasing' with 'non-increasing'.
- Misapplying the term to discrete sets without defining the order.
- Writing 'strictly decreasing' for a function that only decreases on part of its domain.
FAQ
Frequently Asked Questions
A 'decreasing' (or non-increasing) function allows the output to stay the same (f(x₁) ≥ f(x₂)). A 'strictly decreasing' function requires the output to always get smaller (f(x₁) > f(x₂)).
No. By definition, a 'strictly' decreasing function cannot have a horizontal (flat) section, as that would mean the output is equal for two different inputs.
Yes, for all real numbers. If x₁ < x₂, then f(x₁) = -x₁ > -x₂ = f(x₂).
Almost exclusively in mathematics and related technical fields like theoretical economics, physics, and computer science, particularly in calculus, analysis, and when discussing monotonicity.
A mathematical function where, as the input value increases, the output value always decreases (the inequality is strict: f(x₁) > f(x₂) for all x₁ < x₂).
Strictly decreasing function is usually technical / academic (primarily mathematics) in register.
Strictly decreasing function: in British English it is pronounced /ˈstrɪktli dɪˈkriːsɪŋ ˈfʌŋkʃən/, and in American English it is pronounced /ˈstrɪktli dɪˈkriːsɪŋ ˈfʌŋkʃən/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think of a slide that only goes DOWN, never flat. 'Strictly' means it's strict about never taking a break—it's always descending.
Conceptual Metaphor
A ONE-WAY DOWNHILL PATH (The input is a journey along a path; the output is the altitude, which only ever decreases as you walk forward).
Practice
Quiz
Which of the following best describes a 'strictly decreasing function'?