Let $A$ be a subset of $\N$. Suppose:
- \[0 \in A.\]
- \[\forall n\in A : n+1\in A.\]
Then $A=\N$.
Proof.Otherwise, $\min\N\setminus A$ would be a limit ordinal, contrary to N#PROP-LO.
Let $A$ be a subset of $\N$. Suppose:
- \[0 \in A.\]
- \[\forall n\in A : n+1\in A.\]
Then $A=\N$.
Proof.Otherwise, $\min\N\setminus A$ would be a limit ordinal, contrary to N#PROP-LO.