diff --git a/submission_thesis/appendixes/algorithmic.tex b/submission_thesis/appendixes/algorithmic.tex
index 4c1b683..9811c66 100644
--- a/submission_thesis/appendixes/algorithmic.tex
+++ b/submission_thesis/appendixes/algorithmic.tex
@@ -26,7 +26,7 @@ The FMMD process is described in chapter~\ref{sec:chap4}.
  \item collection of components to form {\fgs},
  \item applying FMEA to the {\fgs},
  \item collecting common symptoms from the FMEA results,
- \item creating a {\dc} representing the failure mode behaviour of the {\fg}.
+ \item creating a {\dc} modelling the failure mode behaviour of the {\fg}.
 \end{itemize}
 %
 \fmmdgloss
@@ -283,10 +283,13 @@ The algorithm, represented by the symbol `$\derivec$', is described using five a
 The symptom abstraction process allows us to take a {\fg} of components,
 analyse the failure
 mode behaviour and create a new entity, a {\dc} that has its own set of failure modes.
+%
 The checks and constraints applied in the algorithm ensure that all component failure
 modes are covered.
+%
 This process provides the analysis `step' to building a hierarchical failure mode model
 from the bottom-up. 
+%
 \fmmdgloss
 
 
@@ -331,7 +334,9 @@ test cases must next be determined.
 %we now need to determine test cases.
 %
 The test cases are collections of failure modes.
+%
 These can be formed from single failure modes or failure modes in combination.
+%
 Let $\mathcal{TC}$ be the set of all test cases, $\mathcal{F}$ 
 be the set of all failure modes.
 %(associated with the functional group $FG$).
@@ -378,9 +383,9 @@ all failure modes in components in the {\fg} are included in at least one test~c
            component failures are investigated
             with some specially selected combination faults}
   
-   \State   { Let $TC$ be the set of test cases }
+   \State   { Let $TC$ be a set of test cases } \Comment {this set is used to collect the test cases} 
    \State { Let $tc_j$ be a set of component failure modes where $j$ is an index of $J$} 
-   \Comment { Each set $tc_j$ is a `test~case' and $TC = \bigcup_{j \in J} \{tc_j\}$ where $J \in \mathbb{N}_{+}$ }
+   \Comment { Each set $tc_j$ is a `test~case' and $TC = \bigcup_{j \in J} \{tc_j\}$ where $J \subset \mathbb{N}_{+}$ }
   
    \State { $ TC := \emptyset $ } \Comment{Initialise set of test cases}
    \State { $ j := 1 $ } \Comment{Initialise index of test cases}
@@ -437,14 +442,14 @@ all failure modes in components in the {\fg} are included in at least one test~c
   \State { let $f$ represent a component failure mode }
   %\ENSURE { That all failure modes are represented in at least one test case }
   \Ensure { $ \forall f \;such\;that\; (f \in F))    \wedge  (f \in \bigcup TC) $ }
-  \Comment { Check that at each single failure mode is
+  \Comment { Check that at each single failure mode in the {\fg} is
             included as a test case.}
   %\EndIf
   %\If{Double fault checking} 
   \State { let $f1,f2$ represent component failure modes, and $c$ any component in the functional group }
   %\ENSURE { That all failure modes are represented in at least one test case }
   \Ensure { $ \forall f1,f2 \;where\; (f1 \wedge f2) \not\in (\forall c)  \;such\;that\; (f1,f2 \in F))    \wedge  ( \{f1,f2\} \in \bigcup TC)  \wedge ({DoubleFaultChecking} = TRUE)$ }
-  \Comment { If ${DoubleFaultChecking}$ is required, check that all possible double failure modes (see section~\ref{sec:unitarystate}) are included  
+  \Comment { If ${DoubleFaultChecking}$ is required, check that all possible double failure modes in the {\fg} (see section~\ref{sec:unitarystate}) are included  
              as a test cases.}
    \State \textbf{return} $TC$
 \end{algorithmic}
@@ -505,6 +510,7 @@ The analysis is primarily a human activity.
 Calculations or simulations
 are performed to determine how the failure modes in each test case will
 affect the functional~group.
+%
 Ideally field data and/or formal physical testing  should be used in addition to static failure mode reasoning
 where possible.
 %
@@ -525,7 +531,9 @@ A set of
 results corresponding to our test cases is now available. 
 %
 These share a common index value ($j$ in the algorithm description).
+%
 These results are the failure modes of the {\fg}.
+%
 \fmmdgloss
 %Once a functional group has been analysed, it can be re-used in 
 %any other design that uses it.