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What does monotonically mean?

Looking for the meaning or definition of the word monotonically? Here's what it means.

Adverb
  1. In a monotonic manner, pertaining to the Greek system of diacritics which discards the breathings and employs a single accent to indicate stress
  2. (mathematics) In a monotonic manner, of a function that either never decreases or never increases as its independent variable increases
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That is, the sequence of numbers of pebbles removed on each turn is a monotonically nonincreasing sequence.
The relationship between attenuation level and wavelength is linear such that the slope of the attenuation vs. wavelength is constant and monotonically increasing or decreasing.
Because he never spent any money, his bank balance increased monotonically.
Structural capital to sectoral GDP rose from 1961 to 1975, before falling monotonically.
The average bias appears to increase monotonically with the maturity of the futures contract, but is significantly different from zero at only the 12-month horizon.
We know that global climate doesn't respond monotonically – it does go up and down with natural variation.

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