Causality, Region of Convergence and which side is the system on I want to try to summarize some relationships between z transform, ROC and causality. But I am getting confused between left/right sided sequences, the ROC and causal. 


If you need stability then the ROC must contain the unit circle. I can understand that.
If you need a causal system then the ROC must contain infinity and the system function will be a right-sided sequence. I am fine with  that too.
If you need an anticausal system then the ROC must contain the origin and the system function will be a left-sided sequence. Yes that's fine.
If you need both, stability and causality, all the poles of the system function must be inside the unit circle.


But #4, doesn't it violate number 2 because we don't include infinity?

Got it from here: http://en.wikipedia.org/wiki/Z-transform#Example_2_.28causal_ROC.29

Thanks
If you combine the two requirements (stability => the unit circle must be inside the ROC), and causality (the ROC is given by $|z|&gt;r$ with some real-valued radius $r$), then it follows that $r&lt;1$ must be satisfied. This means that the ROC is outside a circle with radius $r&lt;1$, and, consequently, all poles must be inside this circle with radius $r&lt;1$. So all poles are inside the unit circle (because, by definition, there are no poles in the ROC).