diff --git a/submission_thesis/CH5_Examples/software.tex b/submission_thesis/CH5_Examples/software.tex
index 1374e48..1fc2164 100644
--- a/submission_thesis/CH5_Examples/software.tex
+++ b/submission_thesis/CH5_Examples/software.tex
@@ -225,7 +225,9 @@ Let us define any value outside the 4mA to 20mA range as an error condition.
 As we read a voltage, we use Ohms law~\cite{aoe} to determine the mA current detected: $V=IR$, $0.004A * \ohms{220} = 0.88V$
 and $0.020A * \ohms{220} = 4.4V$. 
 %
-Our acceptable voltage range is therefore 
+Our acceptable voltage range\footnote{For the purpose of clarity we are ignoring resistor tolerance
+for this example. In a practical {\ft} reader we would factor in resistor tolerance to the limits, or 
+allow `deadbands' of $\approx \half mA$ at either end of the range.} is therefore 
 
 $$(V \ge  0.88) \wedge (V \le 4.4) \; .$$ 
 
diff --git a/submission_thesis/style.tex b/submission_thesis/style.tex
index 5a3964f..520bf9c 100644
--- a/submission_thesis/style.tex
+++ b/submission_thesis/style.tex
@@ -55,6 +55,8 @@
 \newcommand{\irl}{in~real~life}
 \newcommand{\enc}{\ensuremath{\stackrel{enc}{\longrightarrow}}}
 \newcommand{\pin}{\ensuremath{\stackrel{pi}{\longleftrightarrow}}}
+\newcommand{\half}{\ensuremath{\frac{1}{2}}}
+
 %
 % OK after about 3 years its not rigorous FMEA (RFMEA) anymore, oh no, its Exhaustive FMEA
 % but since the fuckers might change it yet again, I am making this a macro.