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How to read the following mathematical expression?

$$\text{For any strictly increasing function } f:\Bbb R\to \Bbb R, v(x)=f(u(x))$$

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The key bits:

"Strictly increasing function" means that for any $x_1 < x_2$, $f(x_1) < f(x_2)$.

"$f:\mathbb{R} \rightarrow \mathbb{R}$": $f$ is a function whose input is a real number, and whose output is a real number.

"$v(x) = f(u(x))$": The transformation $v$, applied to a real number $x$, gives the same result as applying the transformation $u$ to $x$ and then using the transformed value as the input to $f$.

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  • $\begingroup$ Sounds correct. $\endgroup$
    – user508281
    Oct 14 '19 at 22:11
  • $\begingroup$ It would help if there was a bit of context around what u and v are, but what I've written is a translation of as much as the snippet you posted covers. $\endgroup$
    – ConMan
    Oct 14 '19 at 23:43
  • $\begingroup$ u represents a utility function. This is from microeconomics. So, u(x) is utility obtained from consuming good x. $\endgroup$
    – user508281
    Oct 17 '19 at 23:14
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"For any strictly increasing function whose name is $f$ which is a function from the reals to the reals, you have that the result of $v(x)$ is the same as the result of $f(u(x))$"

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