For example, how would I show that a variable is equal to a single item in a set which meets a certain condition?
Is set builder notation the best way?
E.g. $b = \{a \in A | f(a) = 3 \}$
The reason I am introducing an equality is because in my desired use case I am writing up some research, and I want to save space when writing further expressions with the item that I am pulling out of the set (so I can just use $b$ in the place of $\{a \in A | f(a) = 3 \}$ for example).
I'm not sure about using set builder notation because I thought it might imply that $b$ is a set when it is intended to be a single item.
Or should I perhaps write it like a sentence?
E.g. $b = a \in A$ where $f(a) = 3$.
I'm really not sure. If there are multiple ways of doing this it would be good to know some of the conventions. But ultimately I would like to be able to express this as succinctly as possible.
Best Answer
If you're just trying to introduce a term that stands in for an arbitrary element of $A$ that satisfies the condition, you'd just want to use something like "$a\in A$ where $f(a)=3$".
You definitely would not want to use set builder notation like the first example, as this would be the subset of $A$ of all those things that satisfy $f(a)=3$. And using $b$ in the second example just adds a second variable that you don't really use.