Solution To Moderate Exercise Number One

(1) Using the basic rules BR1 - BR12, show that the following property of real numbers holds:

 1 + 1  0

SOLUTION:

1 > 0 (by introductory exercise 6)

implies

( 1 + 1 ) - 1 > 0

which implies

1 + 1 > 1.

But 1 > 0. So 1 + 1 > 0 as well(by introductory exercise 5), and by BR-10 this means that 1 + 1 not equal to 0.