1396 

  1396 

  1397   While formalising the chapter in \cite{Boolos87} about universal

  1397   While formalising the chapter in \cite{Boolos87} about universal

  1398   Turing machines, an unexpected outcome of our work is that we

  1398   Turing machines, an unexpected outcome of our work is that we

  1399   identified an inconsistency in their use of a definition. This is

  1399   identified an inconsistency in their use of a definition. This is

  1400   unexpected since \cite{Boolos87} is a classic textbook which has

  1400   unexpected since \cite{Boolos87} is a classic textbook which has

  1402   idea about Turing machines is that when started with standard tapes

  1404   idea about Turing machines is that when started with standard tapes

  1403   they compute a partial arithmetic function.  The inconsitency arises

  1405   they compute a partial arithmetic function.  The inconsitency arises

  1404   when they define the case when this function should \emph{not} return a

  1406   when they define the case when this function should \emph{not} return a

  1405   result. They write in Chapter 3, Page 32:

  1407   result. They write in Chapter 3, Page 32:

  1406 

  1408