Two halves equal two? (How to double your money!)

An odd guy I assume is homeless brings a cup of coffee and a snack to the register and I ring it up: $1.98. He hands me what I at first think is $2.00 but it's a dollar bill ripped in half.

ME: "Do you have another dollar?"
ODD GUY: "That is two."
ME: "No, sorry, but it's two halves of one."
ODD GUY: "The law says it's still a valid dollar if at least half remains."
ME: "That can't be true, it would have to be more than half don't you think?"
ODD GUY: "No, half is still good."
ME: "So I could tear hundred dollar bills in half to make them worth $200. and double my money?"
ODD GUY: "I guess so."
ME: "You could teach Warren Buffet a thing or two!"

He smiles. Awkward silence.

ME: "Look, I was getting ready to dump the coffee soon and clean the pots. Take it, and keep your dollar . . .or two. The candy's on me."
ODD GUY: "Thank you, Sir!"
ME: "No problem, have a great night."