What is a two dimensional sphere in a three dimensional space?

Question

I was reading about Hausdorff paradox and i met this statement "It involves the sphere S2 (a 2-dimensional sphere in R3)" and i don't know what it means or how it appears in a paper P.S I am a novice mathematician. Thank you ye mathematicians..! ;a https://en.wikipedia.org/wiki/Hausdorff_paradox;

Answer 1

The definition of a $n$-sphere centered at $y \in \mathbb{R}^{n+1}$ is simply: $$\Bbb S^n = \left\{{x \in \mathbb{R}^{n+1} : \left|{x - y}\right| = r}\right\}$$

So that a two dimensional sphere is simply the 2D surface of an "ordinary" ball in three dimensional space.