MathDB

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.

Problem Statement