Steven D'Aprano <[email protected]>:
> That's not the case. It's not so much that they stopped trying (implying
> failure), but that they succeeded, for some definition of success (see
> below).
>
> The contemporary standard approach is from Zermelo-Fraenkel set theory:
> define 0 as the empty set, and the successor to n as the union of n and the
> set containing n:
>
> 0 = {} (the empty set)
> n + 1 = n ∪ {n}
That definition barely captures the essence of what a number *is*. In
fact, there have been different formulations of natural numbers. For
example:
0 = {}
1 = {0}
2 = {1}
3 = {2}
etc
Marko
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