a definition eminently fitted to give an idea of the number 1 to persons who had never heard speak of it.
I understand Peanian too ill to dare risk a critique, but still I fear this definition contains a petitio principii, considering that I see the figure 1 in the first member and Un in letters in the second.
However that may be, Burali-Forti starts from this definition and, after a short calculation, reaches the equation:
which tells us that One is a number.
And since we are on these definitions of the first numbers, we recall that M. Couturat has also defined 0 and 1.
What is zero? It is the number of elements of the null class. And what is the null class? It is that containing no element.
To define zero by null, and null by no, is really to abuse the wealth of language; so M. Couturat has introduced an improvement in his definition, by writing:
