increasing monotonic
Definition
- 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.
Adjective
-
consistently increasing
-
an increasing monotonic function
-
