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I wonder if there exists a symbol with which we could express that a variable $y=y(x)$ is monotonic with respect to $x$. In a similar way that the $\propto$ symbol expresses proportionality but in a wider sense, without requiring a linear dependence.

Quaerendo
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    While this comment doesn't answer the question, I feel it important to remind folks that symbols are not inherently better than words in mathematics—words are a crucial part of mathematical writing and shouldn't be avoided. Simply writing "$y$ is a monotonic function of $x$" is excellent communication. – Greg Martin May 30 '19 at 15:52
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    No doubt you are right, I asked this because I'm a little puzzled with the fact that the $\propto$ symbol exists but there isn't another one with a wider sense. I actually was seeking for that symbol in order to try to write class notes faster (because I often have to use $\propto$ despite I know that the relationship may not be linear...). – Quaerendo May 31 '19 at 07:21

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If it is just to write class notes, you could use $\nearrow$ for a monotonically increasing function and $\searrow$ for a monotonically decreasing function.

J.-E. Pin
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