Base120 · Inversion

Inverse/Proof by Contradiction

IN · Inversion

Assume a claim is false, derive logical impossibility, thus proving the claim true

Model code
IN6
Transformation
IN (Inversion) — Improve by removing, reversing, or stress-testing assumptions.
Priority
6 of 20
Framework
HUMMBL Base120 — 120 mental models across 6 transformations

When to use

"Use when direct proof is difficult. Assume the claim is false, derive a logical impossibility, and conclude the claim must be true. A foundational technique in mathematics and formal logic."

Example

"To prove no algorithm can sort n items faster than O(n log n) in the general case, assume such an algorithm exists, show it would require fewer comparisons than there are possible permutations (a contradiction), thus no such algorithm exists."

Common misuse

"Using contradiction informally — deriving not an impossibility but merely an improbability or undesirability. Proof by contradiction requires logical impossibility, not just unlikeliness."

Also known as

Proof by ContradictionReductio ad Absurdum

Related models

IN8IN4DE4