What does monotonically mean?
Monotonically means in a steady, unchanging manner, usually describing a quantity that rises, falls, or otherwise develops without reversing direction. The term is especially common in mathematics, statistics, economics, and technical writing, where it describes a monotonic function or sequence: one that never increases and then decreases, or vice versa. In everyday usage, it can convey that something progresses at a consistent rate, although it may sound more technical than steadily or consistently. Monotonically does not necessarily imply that the change is rapid or dramatic; a gradual increase can be monotonic. It also does not by itself mean that the subject is dull, though the related adjective monotonous can describe something lacking interest or variety.
adverbIn a steady, unchanging way, especially without increases or decreases in value, intensity, or variation.
- In a steady, unchanging manner, especially without variation in direction, value, or intensity.
"The temperature rose monotonically throughout the afternoon."
"The river's depth decreased monotonically as the drought continued."
"Her fortunes improved monotonically after she began training for the national exam."
A function can climb every day and still be monotonic: the key is that it never reverses direction.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does monotonically come from?
The word comes from the Greek roots monos, meaning “single,” and tonos, meaning “tone” or “pitch.” Through English derivatives such as monotony, monotone, and monotonous, it developed the sense of something having only one level or course. The adverb monotonically was formed from the related English adjective monotonic.
Related word forms
How monotonically is actually used
This word is formal and particularly common in mathematics, statistics, economics, and technical descriptions of change. In general prose, steadily or consistently may sound more natural.
Easily confused with monotonically
Both words mean in a dull or unchanging manner, but monotonically is especially common in technical contexts such as mathematics and data analysis.