monotone function
A "monotone function" is fundamental in mathematics, especially in calculus and order theory, describing functions that preserve or reverse order.
🇺🇸 US Voice:
🇬🇧 UK Voice:
Definition
C1Calculus
(technical, academic)A function that is either entirely non-increasing or entirely non-decreasing.
Example
- In calculus, a monotone function simplifies the analysis of limits and continuity.
C2Order Theory
(technical, academic)A function between ordered sets that either maintains or reverses the order of elements.
Example
- Order theory uses monotone functions to study the structure of ordered sets.
C2Boolean Algebra
(technical, academic)A function where changing an input from 0 to 1 results in either no change or a change from 0 to 1 in the output.
Example
- In Boolean algebra, a monotone function is crucial for simplifying logical expressions.
Similar
Terms that have similar or relatively close meanings to "monotone function":