The ProofQuest cast
Each friend shows you one idea by how they act. Meet them all and see how the ideas fit together.
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Direct-Proof Dora Direct proof: assume premises, derive conclusion by straightforward logical steps -
Induction Ida Weak / standard mathematical induction: base case + inductive step -
Strong-Induction Sten Strong induction: base case + assume all prior cases hold -
Contradiction Cassius Proof by contradiction (reductio ad absurdum): assume the negation, derive a contradiction -
Contrapositive Cara Proof by contrapositive: prove "not Q → not P" to establish "P → Q" -
Construction Cole Proof by construction: prove existence by explicit construction of an example -
Pigeonhole Perch Pigeonhole principle: if n+1 items are placed in n bins, at least one bin contains 2+ items -
Exhaustion Edda Proof by exhaustion / cases: enumerate every case and verify each -
Counterexample Cricket Disproof by counterexample — one exception topples a universal claim -
Biconditional Bex Biconditional proof — proving 'if and only if' in both directions -
Uniqueness Una Proof of uniqueness — suppose two, show they must be the same one -
QED Closing-mark mentor — the ∎ at the end of every proof; the gentle voice that names completion + invites the next problem