Let the continuous functions f_n(x), \; n\equal{}1,2,3,..., be defined on the interval [a,b] such that every point of [a,b] is a root of f_n(x)\equal{}f_m(x) for some n \not\equal{} m. Prove that there exists a subinterval of [a,b] on which two of the functions are equal. functionreal analysisreal analysis unsolved