How does a 0-ball have volume 1?

Question

I've been reading about n-balls and I found in the Wikipedia article that in dimension 0, the volume of a 0-ball is 1. I have searched for more information but I can't find any resource explaining this.

So, how does a 0-ball have volume 1?

Answer 1

$0$-dimensional space is just a single point and every ball of positive radius contains that point. Moreover, the measure in this space is just the counting measure. So the volume of the ball is $1$ because it contains one point.

Answer 2

They don't. There are no zero-dimensional balls. the Wikipedia article is not precise. The reason for the imprecision can be filed under "semantic sugar": it so happens that if you plug $n=0$ in the formula for the volume of an $n$-dimensional ball, where $n\geq 1$, you get $1$.