The act of providing or using an example; illustrating by means of an example.
From example (noun) used as a verb + -ing (present participle). English readily converts nouns into verbs, and example has been used verbally since at least the 15th century.
The verb 'to example' is grammatically sound but feels awkward to modern speakers who prefer 'exemplify' or 'illustrate with examples'—it shows how English naturally selects certain word forms and abandons others based on how common they become in actual speech.
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