Simple assignment notation question

Question

this is an elementary question, but I haven't encountered this notation before:

S, and T are being assigned but what does "/" signify here?

Thanks

Answer 1

These both signify a quotient of $\mathbb{R}$ with respect to certain group actions. The group $(\mathbb{Z},+)$ acts on $\mathbb{R}$ via $(n,x) \mapsto n+x$. The orbit $\mathcal{O}_x$ of a point $x$ is the set $\{x+n \mid n \in \mathbb{Z}\}$ and the quotient $\mathbb{R}/\mathbb{Z}$ is the set $\{\mathcal{O}_x \mid x \in \mathbb{R}\}$. The orbit of any integer is just $\mathbb{Z}$ and each noninteger is in the orbit of exactly one point in the unit interval $(0,1)$, so if we identify points which are in the same orbit, we get the unit interval with the endpoints identified.