If three mutually unequal rational numbers can be expressed in the form of 1, a, a + B, or 0, B,

If three mutually unequal rational numbers can be expressed in the form of 1, a, a + B, or 0, B,

There are three cases
(1) B = 1 can be divided into two cases, a = 0 or a + B = 0
(a) When a = 0, a + B = 0 + 1 = 1, then these three numbers are 1,0,1, because these three numbers are not equal rational numbers, so this situation does not hold
(b) When a + B = 0, a = - B = - 1, then the three numbers are 1, - 1,0, so they can be expressed as 0, B, - B
(2) B = a because 1 is not equal to 0, so it can only be a + B = 0, then a = - B. It is contradictory to B = a
(3) If B = a + B, then a = 0. Then these three numbers are 1, 0, B, and can be expressed as 0, B, 1