doc: fix typos

diff --git a/doc/implementation.tex b/doc/implementation.tex
index bdacc57..95166ef 100644 (file)
--- a/doc/implementation.tex
+++ b/doc/implementation.tex
@@ -482,7 +482,7 @@ T \subseteq R \cup \left(R \circ T\right)
 $$
 This is essentially Theorem~5 of \shortciteN{Kelly1996closure}.
 The only difference is that they only consider lexicographically
-forward relations, a special case of acyclic relation.
+forward relations, a special case of acyclic relations.
 
 If, on the other hand, $R$ is cyclic, then we have to resort
 to checking whether the approximation $K$ of the power is exact.
@@ -812,7 +812,7 @@ k \, \vec L \le \vec j - \vec i \le k \, \vec U
 $$
 However, when we intersect domain and range of this relation
 with those of the input relation, then the result only contains
-the idenity mapping on the intersection of domain and range.
+the identity mapping on the intersection of domain and range.
 \shortciteN{Kelly1996closure} propose to intersect domain
 and range with then {\em union} of domain and range of the input
 relation instead and call the result $R_i^?$.