In the context of the Axiom of Foundation: clarifying the text's discussion of the least element

Question

In Stillwell's "Real Numbers," page 133, he says the least element in a ordinal $\sigma$ is $0$ or (using von Neumann's concept of natural numbers) the empty set $\{\}$.

My question is on the subsequent remark:

the least element in $\sigma - \{0\}$ is $\{0\}=1$.

I hope this is a typo, and he really means: the least element in $\sigma - \{\}$ which is $\{0\}=1$.

Thanks

Answer 1

Here $\sigma-\{0\}$ is the set of elements of $\sigma$ that are not elements of $\{0\}$, that is, the set of elements of $\sigma$ that are not equal to $0$. The remark in the text says that $1$ is the least element of $\sigma$ which is not $0$.