Induction

🅟 Mar 06, 2026

  🅤 Mar 08, 2026

PROP-IDC. Induction.

Let $A$ be a subset of $\N$. Suppose

  1. \[0\in A;\]
  2. \[\forall n\in A:n+1\in A.\]

Then $A=\N$.

Proof.Otherwise, $\min\N\setminus A$ would be a limit ordinal, contrary to PROP-N-LO.