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All grown-ups were once children, but only few of them remember it

"Toutes les grandes personnes ont d'abord été des enfants. (Mais peu d'entre elles s'en souviennent.)" [All grown-ups were once children... but only few of them remember it.] Antoine de Saint-Exupéry, "Le Petit Prince." An impromptu game of "who can name the largest number?" is an example I often point to as a way in which young children teach each other about non-trivial mathematical ideas and facts, such as infinity and the concept of proof by contradiction (embodied in this case by one child eventually realizing that they can defeat any other child's guess by adding "plus one" to that guess, thus demonstrating by contradiction* that there is no largest natural number). Prematurely putting such games to an end by immediately providing the nominal goal --- for instance, providing these children with a brief lecture on infinity and the unbounded nature of the natural numbers --- defeats the entire "purpose" of such curiosity-driven play, insofar as play *has* a purpose: to explore, to learn, to develop, and to simply have fun. * - to be pedantic, this is a proof by negation rather than a proof by contradiction, but that distinction is not the point of the anecdote I wish to make. (1/3)

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