And isometry does not need to be a bijection.
It just needs to preserve distances.
My textbook says that
For n>=2, consider the set
with metric induced by d (usual metric). Then is a subset of and is isometric to under correspondence
(a)
My question is
Isometry should be a bijective function between and . (a) does not look bijective for me if each in maps to in . ( how do we map 0? it should be bijective by definition of isometry)