[
P{text{ever enter} jrvert text{start in} i}
= Pbigg{bigcup_{n=0}^{infty} {X_n = j biggrvert X_0 = i bigg}
& leq sum_{n=0}^{infty} P{X_n = j rvert X_0 = i}
& = sum_{n=0}^{infty} P_{ij}^{n}
& = 0
]