# What does the steady state represent to a Markov Chain?

I'm a little confused as to the interpretation of the steady state in the context of a Markov chain. I know Markov chains are memoryless, in that each state only depends on its immediate predecessor, but doesn't that mean the system is in a sort of steady state?

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Thank you @Lucius - Mods please feel free to delete both of these comments. –  leonardo Sep 11 '12 at 23:31
Some Markov chains do not have stable probabilities. For example, if the transition probabilities are given by the matrix $$\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix},$$ and if the system is started off in State 1, then the probability of finding the system in State 1 will oscillate between 0 and 1 forever.