Monotonous function or monotonic function

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I am from a non-English speaking country. Should we say monotonous function or monotonic function?

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That would be monotonic function. Monotonic is always used in relation to the function you are talking about.

http://mathworld.wolfram.com/MonotonicFunction.html

Monotonic describes something this is unchanged or altered, such as the function in maths whereas Monotonous describes something lacking in variety and is usually used in reference to tone.

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"Monotonic" or "monotone", but not "monotonous" (boring).

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monotonic for sure is to be used. Monotonic functions are those functions which are either increasing or decreasing. They are such that for each specific value of x there is a unique y(value of function) which does not repeat for any other x.