If I have a unit ball in space $R^d$ then in how many dimension space its surface will be represented. I know the answer is d-1 but i am unable to convince myself. can anybody give me some intuition. I also did'nt got one line from wikipedia
In mathematics, a distinction is made between the sphere (a two-dimensional closed surface embedded in three-dimensional Euclidean space) and the ball (a three-dimensional shape that includes the interior of a sphere).
and can you give me some reference so that i can understand this topic well means what are the property of ball in $R^d$ why people use them in proof,etc.
I know this is very broad but you can narrow down to any level. I want to collect as much info as i can