Meaning & use
monotonically
Last updated
Meanings
adverbnot comparablemathematics
In a way that only ever moves in one direction, rising or falling, without reversing.
Grammar: Describes the behavior of a value or function: increase monotonically.
Patterns
- increase monotonically
- decrease monotonically
The function increases monotonically as x gets larger.
The temperature fell monotonically through the night.
A sorted list of numbers grows monotonically from left to right.
adverbnot comparabletechnical
In a way that follows one trend through a data set or process, never changing course, as used in statistics and computing.
Grammar: A looser use outside strict mathematics, often in data analysis.
Patterns
- rise monotonically
- shrink monotonically
Sales rose monotonically for six quarters.
The error shrank monotonically with each training round.
The cost per unit fell monotonically as production grew.
Common combinations
- increase monotonically
- The sequence increases monotonically.
- decrease monotonically
- The error decreases monotonically over time.
- vary monotonically
- The output varies monotonically with the input.
- converge monotonically
- The series converges monotonically to zero.
- grow monotonically
- The curve grows monotonically but flattens.
Synonyms and how they differ
- steadily
- Steadily means at an even rate, while monotonically only requires moving one way, not at a constant pace.
- consistently
- Consistently suggests regular repetition, whereas monotonically is about direction of change only.
- uniformly
- Uniformly suggests the same amount everywhere, which monotonic change does not require.
Opposites
Word family
- monotonic adjective
- always moving in one direction, either up or down
- monotonicity noun
- the property of being monotonic
- monotone adjective
- staying the same or moving in one direction
- monotonous adjective
- dull because of lack of variety
Commonly confused: monotonically or monotonously?
monotonically vs monotonously
Monotonously means in a dull, repetitive way, whereas monotonically describes steady movement in one direction.
Practice
The value rose from 1 to 2 to 5 to 9 and never went down. Which adverb describes this?
Choose one answer.
Monotonically means moving only in one direction. Monotonously means dully, which is the tempting wrong option, and erratically and cyclically describe other patterns.
Make it your own
Write a sentence using “monotonically”, then check it and compare it with the examples above.