Link to current text
MATH.22:3 - Forces
| Force | Tension |
|---|
| Generality | Fewer assumptions can cover more structures while supporting fewer conclusions. |
| Stronger constructions | Added axioms can supply an object or simplify a proof while excluding intended cases. |
| Familiar notation | A new symbol can abbreviate an existing construction or introduce a new assumption. |
| Proof reuse | A theorem may remain valid even when its familiar proof uses a removed axiom. |
| Useful metatheory | A small countermodel can settle a local question; a consistency claim about a foundation can require much stronger work. |
| Computational use | An existence principle can support a mathematical argument while leaving an obtaining procedure to be supplied. |