would evaluate as many cases as needed to sufficiently prove or provide convincing evidence that the thing in question is true. Sometimes this involves evaluating every possible case (where it is also known as proof by exhaustion). by example A proof by example is an argument whereby a statement is not proved but instead illustrated by an example. If done well, the specific example would easily generalize to a general proof. by inspection A rhetorical shortcut made by authors who invite the reader to verify, at a glance, the correctness of a proposed expression or deduction. If an expression can be evaluated by straightforward application of simple techniques and without recourse to extended calculation or general theory, then it can be evaluated by inspection. It is also applied to solving equations; for example to find roots of a quadratic equation by inspection is to 'notice' them, or mentally check them. 'By inspection' can play a kind of gestalt role: the answer or solution simply clicks into place. by intimidation Style of proof where claims believed by the author to be easily verifiable are labelled as 'obvious' or 'trivial', which often results in the reader being confused. clearly, can be easily shown A term which shortcuts around calculation the mathematician perceives to be tedious or routine, accessible to any member of the audience with the necessary expertise in the field; Laplace used obvious (French: évident). complete intuition commonly reserved for jokes (puns on complete induction). diagram chasing Given a commutative diagram of objects and morphisms between them, if one wishes to prove some property of the morphisms (such as injectivity) which can be stated in terms of elements, then the proof can proceed by tracing the path of elements of various objects around the diagram as successive morphisms are applied to it. That is, one chases elements around the diagram, or does a diagram chase. handwaving A non-technique of proof mostly employed in lectures, where formal argument is not strictly necessary. It proceeds by omission of details or even significant ingredients, and is merely a plausibility argument. in general In a context not requiring rigor, this phrase often appears as a labor-saving device when the technical details of a complete argument would outweigh the conceptual benefits. The author gives a proof in a simple enough case that the computations are reasonable, and then indicates that "in general" the proof is similar.