Question

please I need a beginner explanation on what an open ball is

Answer 1

a sphere but includes the inside in solutions, solid sphere kinda

Answer 2

it is a region of points, instead of a surface of points on the sphere

Answer 3

all the points a distance of 0 to less than radius

Answer 4

in a metric space \(X\) equipped with a metric \(d\), an open ball centered at some point \(p\) with radius \(r>0\) is the set of all the points in our space that are within \(r\) distance away from \(p\) as measured by our metric: $$B(p;r)=\{x\in X:d(p,x)<r\}$$