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MATH.10:3 - Forces

ForceTension
Preserved conditionsA convenient change is easy to calculate, but it must retain the constraints used by the conclusion.
Local informationA first-order change can expose a useful direction cheaply; stronger conclusions can require finite changes, further terms or a theorem.
CoverageA small family can reveal an obstruction, while a claim about every candidate needs a reason that the family or argument covers them.
Form of the candidatesDiscrete choices, smooth vectors and histories support different kinds of variation.
Use of the resultA mathematical improvement can guide a decision or a model construction; its application still depends on the meaning of the criterion and constraints.