I’ve been reading e-book ”Introduction to Mathematical Philosophy” originally written by Bertrand Russell and published in the year 1901.
Among other interesting thoughts Russell gives thought to the definition of a number. This is something very interesting; I’ve been thinking myself strange things about number zero. Can zero be considered as a whole number? It doesn’t describe anything existing as whole. If the number of something is zero, this something doesn’t exist at all in somewhere, particularly not as whole.
As to definition of number, Russell discusses about classes. From an old Finnish book that discusses university level algebra, I recently learned the definition of zero as a class. In Russell’s book zero is defined as a class in slightly different way: Russell doesn’t say anything about the empty set, instead he mentions ”null-class”. I think I will read this part of the book over and over again.
This is something fascinating…
Hopefully you got interested in this great book: