Notation to mark which variables a function is dependent of?

Asked Dec 23 '16 at 17:39

Active Dec 23 '16 at 17:39

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If I have a function $f$, how do I mark the variables of a function, without going through the hassle of formally constructing it like this;

$$\begin{array}{l}f:&A\to B\\&\color{green}{(x_1;x_2;...;x_n)} \mapsto f(x_1;x_2;...;x_n) \end{array}$$

If I have the relation $y = x^2+cz+b$, and want to mark that $y$ is a function of $x$, how can I mark this? Apparently $y(x)$ is a value, so that won't do the trick, and $y_x$ is a partial derivative, so I don't see any nice shorthand way of marking it.

asked Dec 23 '16 at 17:39

Frank Vel

5,339

$y(x)$ is the standard way to mark a dependence of $y$ on $x$ explicitly. – Edward Evans Dec 23 '16 at 17:41
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$y(x)$ is a value, but I guess you can easily write down $y(x)=x^2+cz+b$ meaning the $y$ depends on $x$, also, I think I have seen the following somewhere: $y(x_)=x^2+cz+b$, if you had more than one, you'd write $y(x_,z_,w_)$ for example – Euler_Salter Dec 23 '16 at 17:42
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I think there's no standard way to do this. You have to tell from context each time. Some of the popular answers to your popular question at http://math.stackexchange.com/questions/1024280/most-ambiguous-and-inconsistent-phrases-and-notations-in-maths address this very point. – Ethan Bolker Dec 23 '16 at 17:42
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What is wrong with : $y=f(x)$ ? – Mauro ALLEGRANZA Dec 23 '16 at 17:58
@MauroALLEGRANZA Nothing wrong, but that implicitly defines the variable. I'd find it better with an explicit marking. – Frank Vel Dec 23 '16 at 18:41
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See the related post : when did the abuse of notation $y=y(x)$ start ?. – Mauro ALLEGRANZA Dec 23 '16 at 18:46

Notation to mark which variables a function is dependent of?

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