I am soon going to start my first analysis course, which uses 'Baby Rudin' (a.k.a. Principles of mathematical analysis by W. Rudin).
I looked a bit through it and noticed that it does not use the notation for functions $f:X \rightarrow Y$ in the whole text (there is other 'minor' stuff on notation, like the subset/proper subset notation, but I know that notation is used by lots of mathematicians)
Of course I know that mathematical notation isn't the most relevant inside mathematics at all, but I don't want to get lost in future courses.
So I would like to ask, mainly to people who have experience with this text, is this a really important thing? Or would using this notation when writing notes be enough? I don't know if this is a big deal but I don't want to get lost in other courses I take in the future.
(I don't know if the tags are OK, please edit them if they are not)
Since it's a text in real analysis, Rudin seems to leave it unsaid that $\mathbb R$ is almost always the codomain of a function or family if it goes unsaid. (If it's an arbitrary metric space instead of $\mathbb R$, he seems to note it.) It's a bit lazy, but probably par for the course for calculus or real analysis texts. Aside from that, he seems to say things like "$f$ maps $E$ into $Y$" quite a bit, which means exactly $f:E\to Y$.
That's what I noticed from a quick flip through the book. If there are any more specific examples, note the section or page numbers and I'm sure we can explain them. It can be a challenging book to get through, but the notation probably won't keep you up.