Please forgive my ignorance, if I've phrased my question improperly. I'm not sure what the appropriate terminology is; that's the basis of my question. So, I'm not sure if I'm even remotely close in my description of this notation:
I'm wondering what is the proper name for the following notation. Is it function notation? Or part of set notation? None of the mathematics courses I've taken at my college (College Algebra through Calculus II) has used this notation, but I've begun to encounter it in some of the calculus & analysis textbooks I've looked at, and I see it used here and elsewhere on the web.
The other part of my question is, where can I learn more about the following notation (and similar/related notation)? It seems like notation like this should be covered in some course, but I haven't encountered on yet which did cover it:
$$f : \mathbb{R} \to \mathbb{R} \quad \text{ or } \quad f : \mathbb{Z} \to \mathbb{R}$$
I understand this is a form of function notation, but I wasn't sure what to call it, and thus what would make a good google query. When I googled "function notation," of course, the results I got back were about the familiar $y=f(x)$ notation.
Best Answer
$f:A\to B$ means that $f$ is a function, that the domain of $f$ is $A$, and that $f(a)\in B$ for every $a\in A.$.... For example, if you see " for every $f:A\to B$ " it means " for every $f$ such that $f:A\to B$ ". In other words " for every function $f$, with domain $A$ , that maps $A$ into $B$ ".