I'm a little confused with axiom of Archimedes has a proof since it is an axiom. So I'm guessing there's a historical reason that this property of ordered field was given such a name. Is there any material for this?
2026-04-01 03:01:19.1775012479
Source request of axiom of Archimedes
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The term "Archimedean axiom" was introduced by Otto Stolz around 1883. Later, Johan Heiberg noticed that this is closely related to an axiom appearing in Euclid V.4. The term has become commonly accepted since then. It should be noted that none of the European mathematicians from Simon Stevin and until the end of the 19th century used the term in this sense, so in a way the commonly accepted term "archimedean field" is somewhat ahistorical, which does not detract from its usefulness. For details see this article.