I am slightly confused about the diagonal method. Can anyone say if I am mistaken. i is the imaginary unit. 1|1+i 2|1+i+i 3|1+i+i+i 4|1+i+i+i+i 5|1+i+i+i+i+i 6|1+i+i+i+i+i+i 7|1+i+i+i+i+i+i+i 8|1+i+i+i+i+i+i+i+i I will now use the diagonal method and make the number i+1+1+1+1+1+1 ... Therefore the list on the right side isn't complete and is bigger than the naturals. The problem is that the list on the right side is populated by numbers a+bi where b and a are natural and its size is therefore N^2. However N^2 can be put into one to one relation with N and we have a contradiction.