Definition:Monotone (Order Theory)/Real Function
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Definition
This definition continues to hold when $S = T = \R$.
Thus, let $f$ be a real function.
Then $f$ is monotone if and only if it is either increasing or decreasing.
Also known as
A monotone function can also be referred to as a monotonic function.
Monotone is preferred on $\mathsf{Pr} \infty \mathsf{fWiki}$ because it is shorter and has less syllables, and hence is more economical.
Also see
- Results about monotone real functions can be found here.
Sources
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 12.1$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): monotonic function