Contradiction in Your Pocket

You use proof by contradiction every day without calling it that. "Suppose I left my keys at the office — but I unlocked my front door when I got home, so I had my keys. Contradiction. I must have left them somewhere between home and here." That is the same logical move Euclid used.

Detectives, doctors, and debuggers all reason this way: assume a cause, follow the implications, and check if reality matches. When it does not, eliminate that possibility and move on. Sherlock Holmes's famous line — "when you have eliminated the impossible, whatever remains must be the truth" — is proof by contradiction in plain English.