Incorrigible (adjective)

1. Impossible to reform or improve; beyond correction.
2. Not willing to be corrected or improved; obstinate.

Origin:

From latin incorrigibilis, from in- + corrigibilis ("that can be correcte.d")

Examples:

1. The judge deemed the criminal as incorrigible and sentenced him to life in prison.
2. He was an incorrigible optimist, always seeing the best in people.
3. The teacher considered the student incorrigible and gave up trying to teach him.
4. Incorrigible behavior in the classroom will not be tolerated.
5. The company had to let go of an incorrigible employee who refused to follow company rules.