MathDB

We will say that a set of real numbers

A = (a_1,... , a_{17})

is stronger than the set of real numbers

B = (b_1, . . . , b_{17})

, and write

A >B

if among all inequalities

a_i > b_j

the number of true inequalities is at least

3

times greater than the number of false. Prove that there is no chain of sets

A_1, A_2, . . . , A_N

such that

A_1>A_2> \cdots A_N>A_1

.
Remark: For 11.4, the constant

3

is changed to

2

and

N=3

and

17

is changed to

m

and

n

in the definition (the number of elements don't have to be equal).

Problem Statement