Translating to math notation from English specifically from Fundamental Alg. I apologize if this is an incorrectly made question. 1st time posting here.
Anyway, I'm a programmer starting the (very) math heavy Fundamental Algorithms by Donald Knuth. In order to prepare myself for the later "math-y" chapters, I'm taking notes where I translate a piece of text from a section to mathematical notation so I can quickly reference later. My math notation skills are lacking to say the least though. How would one go about translating the below example?
Here is the example (From Section 1.1):
"We have quadruple $(Q,I,\Omega,f)$, in which $Q$ is a set containing subsets $I$ and $\Omega$ and $f$ is a function from $Q$ into itself. Furthermore $f$ should leave $\Omega$ pointwise fixed; that is, $f(q)$ should equal $q$ for all elements $q$ of $\Omega$."
So I want to convert that statement to mathematical notation, I don't have my attempts in front of me I took from last night but I tried starting with expressing "$f(q)$ should equal $q$ for all elements $q$ of $\Omega$." correctly first which I had trouble with:
$$
\{q\in\Omega\vert f(q)=q\}
$$
I'm a little confused with the correct notation for "for all elements" because I've seen the symbol $\forall$ to mean "for all". also I know $\vert$ stands for "such that", it seems like I'd use that in this case but I'm not sure.
My question is, how do you go about translating something like the quote above, and is there any good reference of mathematical notation?
I feel like doing this would make my parsing and grokking of strictly math notation significantly better which is why I'm doing it this way.
 A: To answer the objective part of your question:


*

*"$Q$ is a set containing subsets $I$ and $\Omega$" is the same as $I, \Omega \subseteq Q$

*"$f$ is a function from $Q$ into itself" is the same as $f: Q \rightarrow Q$

*"$f$ should leave $\Omega$ pointwise fixed" is the same as $\forall q \in \Omega,\,f(q) = q$


You have written $\{q\in\Omega\vert f(q)=q\}$ which is the same as "the set of all elements $q$ in the set $\Omega$ such that $f$ maps them to themselves".
To answer the subjective part of your question: I wouldn't recommend trying to 'translate' everything into mathematical notation because that would just make it confusing and hard to understand, even for people who are used to reading mathematical notation. However, it is true that some things are more concisely and/or precisely expressed using mathematical notation, and it is good that you are trying to learn how to do so.
As you come across more and more mathematical notation in e.g. papers or online sources like Math.SE you will learn certain 'idioms' for how things are usually expressed (like @Lubin's comment on the question). A dictionary of sorts can be found here.
