monotonic

Thân thiện

The graph shows a monotonic increase over time.

Definition

1. 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.

Usage Examples

• 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.

Advanced Usage

• "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.

Variants and Related Words

• 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.

Synonyms

• For sound: Unvarying, flat, toneless, droning.
• For mathematics: Consistently increasing, consistently decreasing, order-preserving (in specific contexts).

Antonyms

• For sound: Melodic, modulated, varied, rhythmic.
• For mathematics: Non-monotonic, oscillating, variable.

Học thuật

Adjective

1. sounded or spoken in a tone unvarying in pitch
   • the owl's faint monotonous hooting
2. of a sequence or function; consistently increasing and never decreasing or consistently decreasing and never increasing in value

Từ đồng nghĩa

• flat
• monotone
• monotonous