To prove a statement by contradiction, first assume the statement is false, then try to infer a contradiction from the assumption, so that we can deduce that the original assumption is false, therefore the original statement must be true.
For example, suppose you see some milk in your fridge. You remember that you bought the milk a few days ago at a local grocery store, but you’d like to remember exactly which day it was purchased. An idea pops into your head, and you ask yourself, did I buy the milk on Monday? A split second later, you remember that you were out of town all day Monday, so you couldn’t possibly have bought the milk at a local store that day.
— What can be computed? a practical guide to the theory of computation