# Perspex Machine IX: transreal analysis

```@inproceedings{Anderson2007PerspexMI,
title={Perspex Machine IX: transreal analysis},
author={James Anderson},
booktitle={Electronic Imaging},
year={2007}
}```
• James Anderson
• Published in Electronic Imaging 2007
• Mathematics, Engineering
We introduce transreal analysis as a generalisation of real analysis. We find that the generalisation of the real exponential and logarithmic functions is well defined for all transreal numbers. Hence, we derive well defined values of all transreal powers of all non-negative transreal numbers. In particular, we find a well defined value for zero to the power of zero. We also note that the computation of products via the transreal logarithm is identical to the transreal product, as expected. We… Expand
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#### References

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Perspex Machine VIII: axioms of transreal arithmetic
• Mathematics, Engineering
• Electronic Imaging
• 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 geometryExpand
Perspex machine: VII. The universal perspex machine
It is argued that nullity is as useful to a manufactured computer as zero is to a human computer and provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that have a cardinality no greater than the real-number line. Expand
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• J. A. Anderson
• Medicine, Biology
• Philosophical transactions of the Royal Society of London. Series B, Biological sciences
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