greatest-integer function: meaning, definition, pronunciation and examples
LowHighly Technical
Quick answer
What does “greatest-integer function” mean?
A mathematical function, typically denoted as f(x)=⌊x⌋ or [x], which maps a real number x to the largest integer less than or equal to x.
Audio
Pronunciation
Definition
Meaning and Definition
A mathematical function, typically denoted as f(x)=⌊x⌋ or [x], which maps a real number x to the largest integer less than or equal to x.
In mathematics and computer science, the function that outputs the integer part of a real number by rounding down towards negative infinity. It is used in discrete mathematics, number theory, and algorithm design.
Dialectal Variation
British vs American Usage
Differences
No significant lexical differences. Both regions use 'greatest-integer function' or 'floor function' in technical contexts.
Connotations
Purely technical with no cultural connotations.
Frequency
Extremely low frequency in general language; used only within specialised academic or professional discourse.
Grammar
How to Use “greatest-integer function” in a Sentence
The greatest-integer function of xApplying the greatest-integer functionVocabulary
Collocations
Examples
Examples of “greatest-integer function” in a Sentence
adjective
British English
- We studied the greatest-integer function properties.
American English
- The greatest-integer function graph is a step function.
Usage
Meaning in Context
Business
Virtually never used.
Academic
Used in mathematics, computer science, and engineering courses and literature.
Everyday
Not used.
Technical
The primary domain of use.
Vocabulary
Synonyms of “greatest-integer function”
Strong
Neutral
Weak
Vocabulary
Antonyms of “greatest-integer function”
Watch out
Common Mistakes When Using “greatest-integer function”
- Confusing it with the 'round' function (which rounds to the nearest integer) or the 'ceiling function' (which rounds up).
FAQ
Frequently Asked Questions
Yes, but specifically rounding down towards negative infinity, meaning for negative numbers: ⌊-3.2⌋ = -4, not -3.
It is commonly denoted ⌊x⌋ (floor brackets) or sometimes [x].
It's used in computer science for integer division, in number theory, and in digital signal processing for quantization.
In many programming languages, casting to int truncates towards zero, which differs from the greatest-integer function for negative inputs.
A mathematical function, typically denoted as f(x)=⌊x⌋ or [x], which maps a real number x to the largest integer less than or equal to x.
Greatest-integer function is usually highly technical in register.
Greatest-integer function: in British English it is pronounced /ˌɡreɪt.ɪst ˈɪn.tɪ.dʒər ˈfʌŋk.ʃən/, and in American English it is pronounced /ˌɡreɪt.ɪst ˈɪn.t̬ə.dʒər ˈfʌŋk.ʃən/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think of the function as a floor: it takes you down to the nearest integer below.
Conceptual Metaphor
A step ladder descending; each step is an integer value.
Practice
Quiz
What is another common name for the greatest-integer function?