# How to read the following mathematical notation?

How to read the following mathematical expression?

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

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 $$f$$.

• Sounds correct. Oct 14 '19 at 22:11
• 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. Oct 14 '19 at 23:43
• u represents a utility function. This is from microeconomics. So, u(x) is utility obtained from consuming good x. Oct 17 '19 at 23:14

"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 $$f(u(x))$$"