increasing monotonic

Thân thiện

A graph shows an increasing monotonic function.

Definition

1. Adjective:
   • Consistently increasing: Describes a function, sequence, or trend that always rises and never decreases or stays constant as its input or index increases. It is a specific mathematical term indicating a strictly upward progression.

Usage Examples

• Adjective:
  • The graph shows an increasing monotonic relationship between study time and test scores.
  • For the sequence to be increasing monotonic, each term must be greater than the previous one.

Advanced Usage

• Mathematical Context: Primarily used in mathematics, statistics, and data analysis to describe functions or sequences. It is more specific than simply "increasing," as it excludes the possibility of the values remaining constant.
  • The derivative of an increasing monotonic function is always positive.

Variants and Related Words

• Monotonic increasing: An alternative phrasing with the same meaning.
  • The algorithm requires the data to be sorted in monotonic increasing order.
• Monotonically increasing: The adverbial form, often used to describe how something increases.
  • The values grew monotonically increasing over the observed period.
• Strictly increasing: A synonym that also excludes constant values, emphasizing that each step is a strict increase.

Synonyms

• Strictly increasing: Always becoming greater.
• Ever-increasing: Continually rising (less technical).

Antonyms

• Decreasing monotonic: Consistently decreasing.
• Non-increasing: Not increasing; may decrease or stay constant.

Học thuật

Adjective

1. consistently increasing
   • an increasing monotonic function