Quote Originally Posted by Radar View Post
Believing that something is true/real means that you make an assumption without having any proof one way or the other.
I guess this goes to show that people use words to mean different things. Freshman philosophy will tell you that "knowledge" is "justified true belief", so allows for belief that is actually justified with a proof. There is a wide space between "I believe that Cantor's diagonal argument is valid", based on a careful analysis of the argument, and "I believe in fairies", based on acceptance of folklore.