As an introductory to real analysis, I have been introduced to the formal definition of a function, and that it needs to consist of 3 things.
If $f : X \to Y,$
Then it needs 'A well defined rule that assigns a unique element $f(x) \in Y$ to each $x \in X.'$
This is the third element, ( the other two being the domain and codomain).
I understand what this means, but for me, as I need to remember the definition, it seems a little 'backwards'.
Is the following sentence an equivalent statement, as it makes much more sense to what I see to be the notion of a function?
'A well defined rule that assign each element $x \in X$ to a unique element $f(x) \in Y.$