What is the $\ell^{\infty}$ norm in $R^2$. I read that on a square in $R^2$, given the $\ell^{\infty}$ norm, there are an infinite number of geodesics between any two points. I don't understand this statement.
Is it just $|x-y|_{\ell^{\infty}}=\max(\{|x_1-y_1|,|x_2-y_2|\})$