Function is increasing - mathematical formula

Question

So I have a few tasks like this one from the title:

Function is increasing <- write the mathematical formula corresponding to the following statement

I am not sure of the notation I should use. Is it

$∀x,y\;\; x < y : f(x) < f(y)$

or

$\forall x,y ((x < y) \to (f(x) < f(y)))$

Or are both solutions fine?

Answer 1

The statement $$\forall x,y \; [x < y \implies f(x) < f(y)]$$ is sometimes written more compactly as $$\forall x < y \; [f(x) < f(y)].$$ Both of those are shorthand for $$\forall x \; \forall y \; [x < y \implies f(x) < f(y)].$$