For the first one, which is the easiest, J1= (0, 1/1)= (0, 1) while I1= (0, 1- 1/2)= (0, 1/2). The "Difference", J1\I1= (1/2, 1). For n= 2, J2 (0, 1/2) while I2= (0, 1- 1/3)= (0, 2/3) so J2\I2 is empty.
For the first one, which is the easiest, J1= (0, 1/1)= (0, 1) while I1= (0, 1- 1/2)= (0, 1/2). The "Difference", J1\I1= (1/2, 1). For n= 2, J2 (0, 1/2) while I2= (0, 1- 1/3)= (0, 2/3) so J2\I2 is empty.
Huh. I read it differently, and I get:
Jn\In = {0} U (1/n,n/(n+1)), except for J1\I1, for which I have {0}.