Given any simple set $S$, for example $S \subset \mathbb R$, I want to "add" a single element $x$ to $S$. It doesn't matter whether $x$ is already in $S$, so the union is the right operation to use.
I first expressed this action as follows, but then wondered if that is correct. $$x \cup S$$
Seeing that the symbol $\cup$ denotes the unit of two sets, and that $x$ is not a set but just an element, e.g. just a number, would it be better to write the following? $$\{x\} \cup S$$
Or, doesn't it matter and both notations are used?