Perspex Machine VIII: axioms of transreal arithmetic

@inproceedings{Anderson2007PerspexMV,
  title={Perspex Machine VIII: axioms of transreal arithmetic},
  author={James Anderson and Norbert V{\"o}lker and A. Adams},
  booktitle={Electronic Imaging},
  year={2007}
}
Transreal arithmetic is a total arithmetic that contains real arithmetic, but which has no arithmetical exceptions. It allows the specification of the Universal Perspex Machine which unifies geometry with the Turing Machine. Here we axiomatise the algebraic structure of transreal arithmetic so that it provides a total arithmetic on any appropriate set of numbers. This opens up the possibility of specifying a version of floating-point arithmetic that does not have any arithmetical exceptions and… Expand
38 Citations
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