Proposition 1 (Induction). Let $A$ be a subset of $\N$. Suppose:
- \[0 \in A.\]
- \[\forall n \in A : n + 1 \in A.\]
Then $A = \N$.
Proof. Otherwise, $\min(\N \setdif A)$ would be a limit ordinal, contrary to FINO > Proposition 1.
Pub Mar 06, 2026 Up Jun 10, 2026
Proposition 1 (Induction). Let $A$ be a subset of $\N$. Suppose:
Then $A = \N$.
Proof. Otherwise, $\min(\N \setdif A)$ would be a limit ordinal, contrary to FINO > Proposition 1.