1329 

  1330   \cite[Page 32]{Boolos87}

  1331 

  1332   \begin{quote}\it

  1333   ``If the function that is to be computed assigns no value to the arguments that 

  1334   are represented initially on the tape, then the machine either will never halt, 

  1335   or will halt in some nonstandard configuration\ldots''

  1336   \end{quote}

  1338   This means that if you encode the plus function but only give one argument,

  1339   then the TM will either loop {\bf or} stop with a non-standard tape

  1340 

  1341   But in the definition of the universal function the TMs will never stop

  1342   with non-standard tapes. 

  1343 

  1344   SO the following TM calculates something according to def from chap 8,

  1345   but not with chap 3. For example:

  1346   

  1347   \begin{center}

  1348   @{term "[(L, 0), (L, 2), (R, 2), (R, 0)]"}

  1349   \end{center}

  1350 

  1351   If started with @{term "([], [Oc])"} it halts with the

  1352   non-standard tape @{term "([Oc], [])"} according to the definition in Chap 3;

  1353   but with @{term "([], [Oc])"} according to def Chap 8

  1354