Example
The Halting problem is r.e. but not recursive. Indeed one can run the Turing Machine and accept if the machine halts, hence it is r.e. On the other hand the problem is undecidable.
Some other r.e. language that are not recursive :
- post correspondance problem
- Mortality (computability theory)
- Entscheidungsproblem
Read more about this topic: Recursively Enumerable Language
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