When Buddhism refers to things called the Three Characteristics of Existence, they talk about Dukkha as one of them, unsatisfactoriness; Anicca, or impermanence, as the second; and Anatta, or sometimes referred to as "not self" here, "non-self" is another word. What is the relationship between impermanence and "not self"? It can be a bit understood like this, which is similar to how the Buddha was asking his own son at the time when his son got enlightened. He would say to his son something like this, "Rahula is the eye permanent or impermanent?" Rahula would say, "Impermanent sir." "Now Rahula, something that is impermanent like the eye, does it have a quality of total satisfaction or is it unsatisfactory in its essence?" Rahula said, "It is unsatisfactory sir." "Now Rahula something that is impermanent and unsatisfactory, is it proper to say this is me, this is mine?" And Rahula said, "No it is not proper." So the terms, "this is me, this is mine," and "not self" mean the same thing, the Buddha was talking about Anatta. When you look at it this way, something that is impermanent, something that is unsatisfactory, cannot be an "atta", which is the opposite of Anatta. When you say "not self", "atta" is the word for self, and that means a permanent everlasting self. So something that is impermanent and unsatisfactory simply cannot be a self. Therefore it is not self.