[DMDB] Fix more errors

semester4/dmdb/parts/03_systems/00_query-optimization/01_search-space/01_rewriting-rules.tex

@@ -33,7 +33,7 @@ The following rules were discussed in the lectures:
     \item Natural join operations are associative, so are theta joins (with restrictions)
           \[
               (E_1 \bowtie E_2) \bowtie E_3 = E_1 \bowtie (E_2 \bowtie E_3)
-              \qquad (E_1 \bowtie_{\theta_1} E_2) \bowtie_{\theta_2 \land \theta_3} = E_1 \bowtie_{\theta_1 \land \theta_3} (E_2 \bowtie_{\theta_2} E_3)
+              \qquad (E_1 \bowtie_{\theta_1} E_2) \bowtie_{\theta_2 \land \theta_3} E_3 = E_1 \bowtie_{\theta_1 \land \theta_3} (E_2 \bowtie_{\theta_2} E_3)
           \]
           This allows for joins to be performed in different orders, allowing us to do the most selective first (fewer rows)
     \item Pushdown selection:

semester4/dmdb/parts/03_systems/02_indexing/06_art-trees.tex

@@ -1,4 +1,4 @@
-Adaptive Radix Trees (ARTs) are mainly used to ensure primary key constraints and to speed up point and highly selective queries (selectivity <0.1\%).
+Adaptive Radix Trees (ARTs) are mainly used to ensure primary key constraints and to speed up point and highly selective queries (selectivity $<0.1\%$).
 It can also be manually created using \texttt{CREATE INDEX} and are automatically created for columns with a \texttt{UNIQUE} or \texttt{PRIMARY KEY} constraint.
 
 The above applies to DuckDB, which is often similar to Postgres.