In a Lawvere metric space, \\(I=0\\). So, an identity element is a map \\(\mathrm{id}_x:0\to\mathcal{X}(x,x)\\). In terms of distances, this means that \\(0\geq d(x,x)\\) (since \\(0\\) is the smallest element of \\([0,\infty]\\), this means \\(d(x,x)=0\\) (this was already observed in the text between the definition of a Lawvere metric space as a **Cost**-category and the example of \\(\mathbb{R}\\) as a Lawvere metric space, in chapter 2), which is the statement of definiteness for a Lawvere metric).