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

$\begingroup$

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 ;

$\endgroup$ 1

1 Answer

$\begingroup$

The definition of a $n$-sphere 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.

$\endgroup$

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy