Problem #PRU-100302

Problems Discrete Mathematics Set theory and logic Mathematical logic

Problem

(a) The sum of some numbers is equal to one. Can it be that the sum of the cubes of these numbers is greater than one?

(b) The sum of some numbers is equal to one. Moreover, it is known that each of the numbers is less than one. Can it be that the sum of the cubes of these numbers is greater than one?