2

Part of 2016 Regional Olympiad of Mexico West

Problems(1)

exists a subset S of A with n elements , with irrational sum

Source: Mathematics Regional Olympiad of Mexico West 2016 P2

A

be an infinite set of real numbers containing at least one irrational number. Prove that for every natural number

n > 1

there exists a subset

S

A

with n elements such that the sum of the elements of

S

is an irrational number.

algebracombinatoricsirrational number