This document discusses the differences between belief and proof. It defines belief as a mental attitude that a proposition is true without empirical evidence, while proof provides sufficient evidence to establish something as true. Beliefs are subjective and based on opinion, faith or reason, whereas proof is objective and based on observations and logical conclusions. The document also explains that while beliefs help form our identities and influence behavior, having proof provides a sense of certainty and security. Ultimately, a belief can be considered a real fact if there is proof to support it.