monotonic
- Adjective:
- Sounded or spoken in a tone unvarying in pitch: Describes a sound, especially speech, that lacks variation in intonation or pitch.
- Of a sequence or function; consistently increasing and never decreasing or consistently decreasing and never increasing in value: In mathematics, describes an ordered set of numbers or a function whose values consistently move in one direction (only up or only down) without reversing.
Describing sound:
- The computer-generated voice had a flat, monotonic quality that made it hard to listen to for long periods.
- He delivered the entire lecture in a monotonic drone, causing several students to fall asleep.
Describing mathematical sequences/functions:
- A monotonic increasing sequence, like 1, 2, 3, 4, never goes down.
- The function f(x) = 2x is monotonic because its value always increases as x increases.
"Monotonic transformation": In economics and mathematics, a transformation of a variable that preserves the original order of the data points.
- Applying a monotonic transformation to the utility function does not change the underlying preferences.
"Monotonically increasing/decreasing": A more precise term often used in technical contexts to specify the direction of the monotonic behavior.
- The algorithm guarantees a monotonically decreasing error rate with each iteration.
Monotone (noun/adjective): Often used interchangeably with 'monotonic' when describing a sound, but 'monotone' is more common in everyday language for unvarying speech.
- She spoke in a dull monotone.
Monotonous (adjective): Describes something that is boring because it lacks variety. While related, it is not a technical synonym for the mathematical sense of 'monotonic'.
- The monotonous landscape of the desert stretched for miles.
- For sound: Unvarying, flat, toneless, droning.
- For mathematics: Consistently increasing, consistently decreasing, order-preserving (in specific contexts).
- For sound: Melodic, modulated, varied, rhythmic.
- For mathematics: Non-monotonic, oscillating, variable.
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sounded or spoken in a tone unvarying in pitch
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the owl's faint monotonous hooting
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of a sequence or function; consistently increasing and never decreasing or consistently decreasing and never increasing in value
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