Let $\Sigma$ be a fan in $N_{\mathbb{R}}$ and $X_{\Sigma}$ the corresponding toric variety. The correspondence $\Psi\mapsto D_{\Psi}$ is a bijection between the set of virtual support functions on $\Sigma$ and the set of $\mathbb{T}$-Cartier divisors on $X_{\Sigma}$. Two Cartier divisors $D_{\Psi_{1}}$ and $D_{\Psi_{2}}$ are rationally equivalent if and only if the function $\Psi_{1}-\Psi_{2}$ is linear.