A TM for a recursive language corresponds to our informal notion of an algorithm.
as per Automata Theory, Languages and Computation by Ullman et al. Then there are languages called RE and $L_d$, where there exist TM that halts for accepting strings in the case of RE languages.
This means that we cannot construct a algorithm for RE languages that are not recursive? Then what is the significance of these RE languages from an algorithm point of view.
What confuses me is that for RE language you can construct a TM. So you can construct an algorithm?