Now comes the diagonal stroke of genius. That first decimal place in the list’s first entry, a11, must, of course, be one of the digits from 0 to 9: for example, it is either 5, or not. Cantor asks us to create our own decimal number between 0 and 1 as follows. Like those on the list, it too will begin “0.”, but its first decimal place will be determined by what a11 is. If a11 is 5, our number will have a 6; but if a11 isn’t 5, we put a 5 in the first place of ours.
