Final answer:
Hamlet's erratic speech and behavior, including wordplay and nonsensical statements, as well as strange and unpredictable actions, are signs that he is losing his mind.
Step-by-step explanation:
One sign or example that Hamlet is losing his mind is his speech and behavior, which becomes erratic and disjointed. For instance, when speaking with Polonius, Hamlet engages in wordplay and makes nonsensical statements. He also exhibits strange and unpredictable actions, such as his sudden outburst in Ophelia's presence. These indications suggest that Hamlet is experiencing a mental breakdown.