Problem #PRU-98298

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle

Problem

Some real numbers \(a_1, a_2, a_3,\dots ,a _{2022}\) are written in a row. Prove that it is possible to pick one or several adjacent numbers, so that their sum is less than 0.001 away from a whole number.