 Next Frege had to specify what it was for one natural number to be the successor of another, or the next largest natural number. How might one define what it is for m to immediately succeed n? The answer is found by appeal to concepts F and G, say, that respectively enjoy m and n as their (finite) cardinals. There must be exactly one more object falling under the concept F than there are objects falling under the concept G. And this will consist in there being a one-one correspondence (R, say) between all the Gs and all but one of the Fs. Formally: 