Why is a subset of a undecidable language decidable? I have problems with the understanding why a subset of a undecidable language is decidable. We've proved in the lecture that $HALT$$_T$$_M$$=${$&lt;M,w&gt;$|M is a TM and M halts on input w} is undecidable. Can someone give an example of a subset from $HALT$$_T$$_M$ and explain why it is decidable? Is $\Sigma^*$ a valid subset of $HALT$$_T$$_M$?
An undecidable language is necessarily infinite. A finite subset of it is always trivially decidable.