DES - Definition of 'Reachable State'

Reachable State:

State $j\in \mathcal{X}$ is reachable from state $i\in \mathcal{X}$ if $p_{i,j}(t)>0$ for some $t>0$

This condition is equivalent to the existence of an oriented path from $i$ to $j$ in the graph representation of the CTHMC

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~Example:

State $1$ is reachable by $2$ and $3$. State $2$ is reachable by $1$ and $3$. State $3$ is NOT reachable by any other state.