Notation of sphere in $\Bbb{R}^n$. – math.stackexchange.com

Notation of sphere in $\Bbb{R}^n$. – math.stackexchange.com

In $\Bbb{R}^n$, the sphere centred at $x\in \Bbb{R}^n$ with radius $l$ is
called $S^{n-1}(x,l)$ or an $(n-1)$-sphere. Why do we called it an
$(n-1)$-sphere? It's certainly not defined on ...