\\(R = 0 \text{ if } x \lt0 \\) gives \\( I(R(-0.2)) = 0.0 \nleq -0.2 \\) meaning there is no right adjoint.

Simply mapping negative values to 0 is a good mapping, it is called the left adjoint.

There is a right adjoint for \\( I : \mathbb{N} \rightarrow \mathbb{R}^+ \\) though.

Another, visual, way to think about \\( I(R(x)) \le x \\) is that red arrows cannot bend to the right [what I was trying to say with the picture].

Simply mapping negative values to 0 is a good mapping, it is called the left adjoint.

There is a right adjoint for \\( I : \mathbb{N} \rightarrow \mathbb{R}^+ \\) though.

Another, visual, way to think about \\( I(R(x)) \le x \\) is that red arrows cannot bend to the right [what I was trying to say with the picture].