Speaking for myself only, I would take this sort of shit seriously, and I would get aggressive on this dipshit. I'd gather everything I had on the guy, all contact, all messages, all threats, all account informations, and I would go to the cops and let them have at him.
Fucking rights.
In case no one has noticed, making threats like this is illegal, and for good reason. Sometimes..... just sometimes..... the freak really IS for real and someone wakes up dead.
Sitting there hoping it will go away won't help if the guy is serious. Sorry, I've never been one to sit there and let some fuckwit mess with my mind. Btw, he looks a lot like a guy Whose nose I busted back in the mid-80's. Look at the tell-tale bump on his beak.
