Proof by example

In logic and mathematics, proof by example (sometimes known as inappropriate generalization) is a logical fallacy whereby the validity of a statement is illustrated through one or more examples or cases—rather than a full-fledged proof.

[1][2] The structure, argument form and formal form of a proof by example generally proceeds as follows: Structure: Argument form: Formal form: The following example demonstrates why this line of reasoning is a logical fallacy: In the common discourse, a proof by example can also be used to describe an attempt to establish a claim using statistically insignificant examples.

denotes the formula formed by substituting all free occurrences of the variable

Likewise, finding a counterexample disproves (proves the negation of) a universal conclusion.

In mathematics, proof by example can also be used to refer to attempts to illustrate a claim by proving cases of the claim, with the understanding that these cases contain key ideas which can be generalized into a full-fledged proof.