I find in many places that first came the sequence criterion, on Cauchy's book "Cours d'analyse" but I am not sure. Does any body know anything about that?
Thank you!
2026-03-25 13:33:27.1774445607
What came first, sequence or $\epsilon-\delta$ criterium for limit?
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The $\varepsilon$-$\delta$ formulation of limits (Wikipedia) was anticipated faintly by Fermat, used implicitly by Cauchy, and formalized by Bolzano in 1817. As Xander Henderson indicated in the comments, the notion of a sequence limit (Wikipedia again)—as $n \to \infty$, for instance—is older: anticipated by Archimedes in his method of exhaustion. However, its formalism dates also to Bolzano (in 1816), but it was apparently not much noticed, and it was reformulated by Weierstrass in the 1870s.
See the "History" section of either Wikipedia article for more details.