From 1061fc6f9cc9bf211c63c242097be0a3b5ee8618 Mon Sep 17 00:00:00 2001
From: Henrik Tidefelt <henrikt@wolfram.com>
Date: Tue, 6 Sep 2022 13:29:31 +0200
Subject: [PATCH] Adjust non-normative description of smoothOrder

Closes #3200.
---
 chapters/functions.tex | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/chapters/functions.tex b/chapters/functions.tex
index f27af7c56..cb709e56c 100644
--- a/chapters/functions.tex
+++ b/chapters/functions.tex
@@ -1228,8 +1228,10 @@ \section{Derivatives and Inverses of Functions}\label{derivatives-and-inverses-o
 
 \begin{nonnormative}
 This means that the function is at least C\textsuperscript{smoothOrder}.
-{\lstinline!smoothOrder = 1!} means that the function can be differentiated at least once in order that all output arguments are still continuous, provided the input arguments are continuous.
-If a tool needs the derivative of a function, e.g.\ for index reduction or to compute an analytic Jacobian, the function can be differentiated analytically at least {\lstinline!smoothOrder!} times.
+
+When a tool computes the derivative of a function, e.g., for index reduction or to compute an analytic Jacobian, each differentiation of a function reduces the \lstinline!smoothOrder! by 1.
+The \lstinline!smoothOrder! information can then be used to infer continuity of the resulting differentiated function calls.
+This is a conservative check, however, meaning that a tool may be able to establish continuity of a function call even though the \lstinline!smoothOrder! has been reduced to less than 0.
 \end{nonnormative}
 
 The optional argument {\lstinline!normallyConstant!} of {\lstinline!smoothOrder!} defines that the function argument {\lstinline!IDENT!} is usually constant.