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Continuing with Yakov's comment.

We can construct a left-adjoint function \\( L : \mathbb{R}\to\mathbb{N} \\) to our \\( I : \mathbb{N}\to\mathbb{R}\\) such that

$$L = \begin{cases}
0 & \text{if } x\le0\\\\
\lceil x \rceil & \text{if } x>0
\end{cases}$$

Can we construct a right-adjoint function \\( R : \mathbb{R}\to\mathbb{N} \\) to our \\( I : \mathbb{N}\to\mathbb{R}\\) such that

$$R = \begin{cases}
? & \text{if } x\lt0\\\\
\lfloor x \rfloor & \text{if } x \ge0
\end{cases}$$

...what do we do when \\( x \lt0 \\)?