I want to show that the sequence given by $X_n\sim \text{Bernoulli}(1/2)$ does not converge in probability. This is part (d) of the following question.
Below is the solution I've seen. Shouldn't it be $P(|X_n-X_{n+1}|\leq 1)=1$ because $X_{n}$ and $X_{n+1}$ could both be zero? I don't quite get the argument after that either. Can someone please explain?
