What is "proof by example"

n. (context logic English) A logical fallacy consisting of providing one or more examples as a proof of a more general statement.

Proof by example (also known as inappropriate generalization) is a logical fallacy whereby one or more examples are claimed as "proof" for a more general statement.

This fallacy has the following structure, and argument form:

Structure:

I know that X is such. Therefore, anything related to X is also such.

Argument form:

I know that x, which is a member of group X, has the property P. Therefore, all other elements of X have the property P.

The following example demonstrates why this is a logical fallacy:

I've seen a person shoot someone dead. Therefore, all people are murderers.

The flaw in this argument is very evident, but arguments of the same form can sometimes seem somewhat convincing, as in the following example:

I've seen Gypsies steal. So, Gypsies must be thieves.