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MATH.11:3 - Forces
| Force | Tension |
|---|
| Short calculation and unbounded sequences | One substitution can establish what every step preserves, but only when it covers all allowed steps. |
| Simple expression and useful distinction | A small expression family is cheap to search, while its invariants may leave the target question undecided. |
| Mathematical rule and implementation | Integer, real and modular arithmetic can preserve different expressions under similar-looking updates. |
| Necessary condition and construction | Different invariant values prove impossibility; equal values can leave ordering and enabling conditions unresolved. |
| General preservation and one starting state | An identity valid for every input is reusable, while a particular reachable set can satisfy further relations. |
| Stable reasoning and changed operations | A changed start may require only a new value; a changed transformation can invalidate the preservation proof. |