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.

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