The induction contract
Induction turns an infinite collection of claims into two finite obligations: establish where the chain begins, then prove that truth moves from one case to the next.
To prove a proposition for every non-negative integer, first prove the base case; then assume it holds for an arbitrary value and use that assumption to establish the next value.
The key move is the : you temporarily assume the statement is true for one arbitrary index. That assumption is not the conclusion; it is the input used to prove the next case.
When both obligations hold, every reachable case follows. The argument is structural: it explains why the property propagates, rather than checking examples one at a time.
Knowledge check
What does the induction hypothesis allow you to do?
Illustrative generated content · source faithfulness not yet pipeline-verified