Hello

I'm trying to prove that if f : [a,b] ---> [a,b] is continuos, there exists an x in [a,b] such that f(x) = x

I've formed a sort of geometric proof - if you take the square [a,b] and draw the diagonal down the middle representing the identity function, then any function defined on the interval [a,b] has to intersect the line at least once.

I'm having trouble formalizing it though. Help would be greatly appreciated...