PLAN--

[saga.git] / notation.tex

diff --git a/notation.tex b/notation.tex
index cc44d4a744668e56950f094eabf2695fb82d7f11..f8a512f4084c1fe92c33079deb8d72b33f1a10f5 100644 (file)
--- a/notation.tex
+++ b/notation.tex
@@ -180,7 +180,7 @@ To quote Pettie \cite{pettie:onlineverify}: ``In the field of algorithms \& comp
 Ackermann's function is rarely defined the same way twice. We would not presume to buck
 such a~well-established precedent. Here is a~slight variant.''}
 We will use the definition by double recursion given by Tarjan \cite{tarjan:setunion},
-which is predominant in the literature on graph algorithms:
+which is predominant in the literature on graph algorithms.
 
 \defn\id{ackerdef}%
 The \df{Ackermann's function} $A(x,y)$ is a~function on non-negative integers defined as follows:
@@ -207,8 +207,10 @@ A(4,3) &= A(3,A(4,2)) = A(3,4) = A(2,A(3,3)) = A(2,A(2,A(3,2))) = \cr
        &= A(2,A(2,4)) = 2\tower(2\tower 4) = 2\tower 65536. \cr
 }$$
 
-\para
-Three functions related to the inverse of the function~$A$ are usually considered:
+\paran{Inverses}%
+As common for functions of multiple parameters, there is no single function which
+could claim the title of the only true Inverse Ackermann's function.
+The following three functions related to the inverse of the function~$A$ are often considered:
 
 \defn\id{ackerinv}%
 The \df{$i$-th row inverse} $\lambda_i(n)$ of the Ackermann's function is defined by: