From b1facc70d8e3be75343611c996dfb76a7960bb3c Mon Sep 17 00:00:00 2001 From: wuyangfan Date: Fri, 19 Jun 2026 22:54:52 +0800 Subject: [PATCH] fix typo in Cauchy sequence definition --- content/sets-functions-relations/arithmetization/cauchy.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/content/sets-functions-relations/arithmetization/cauchy.tex b/content/sets-functions-relations/arithmetization/cauchy.tex index 572a316b..03623484 100644 --- a/content/sets-functions-relations/arithmetization/cauchy.tex +++ b/content/sets-functions-relations/arithmetization/cauchy.tex @@ -111,7 +111,7 @@ relations. First we need the idea of a function which tends to $0$ in the limit. For any function $h : \Nat \to \Rat$, say that \emph{$h$ tends to $0$} iff for any positive $\epsilon \in \Rat$ we have that -$(\exists \ell \in \Nat)(\forall n > \ell)|f(n)| < +$(\exists \ell \in \Nat)(\forall n > \ell)|h(n)| < \epsilon$.\footnote{Compare this with the definition of $\lim_{x \mathord{\rightarrow}\infty}f(x) = 0$ in \olref[his][set][limits]{sec}.} Further, where $f$ and $g$ are