# Perspex Machine IX: transreal analysis

@inproceedings{Anderson2007PerspexMI, title={Perspex Machine IX: transreal analysis}, author={James Anderson}, booktitle={Electronic Imaging}, year={2007} }

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

#### 14 Citations

Construction of the Transreal Numbers and Algebraic Transfields

- 2015

The transreal numbers, introduced by James Anderson, are an extension of the real numbers. The four arithmetical operations of addition, subtraction, multiplication and division are closed on the set… Expand

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 geometry… Expand

Transdifferential and transintegral calculus

- Mathematics
- 2014

The set of transreal numbers is a superset of the real numbers. It
totalises real arithmetic by defining division by zero in terms of three def-
inite, non-finite numbers: positive infinity,… Expand

Construction of the transreal numbers

- Mathematics
- 2014

The transreal numbers, proposed by James Anderson, are an extension of the real numbers. This new set is closed under the four arithmetical operations: addition, subtraction, multiplication and… Expand

Perspex machine XI: topology of the transreal numbers

- Mathematics
- 2008

The transreal numbers are a total number system in which even, arithmetical operation is well defined even-where. This has many benefits over the real numbers as a basis for computation and,… Expand

Transreal numbers: Mathematics or Reverie?

- 2014

Mathematics, known as an exact science, has the concept of number as one of its fundamental ideas. Nevertheless history shows that the understanding we have of numbers is not a dogma, but a… Expand

Transreal Calculus

- 2015

Transreal arithmetic totalises real arithmetic by defining division by zero in terms of three definite, non-finite numbers: positive infinity, negative infinity and nullity. We describe the transreal… Expand

Evolutionary and Revolutionary Effects of Transcomputation

- Computer Science
- 2011

This work reviews transreal arithmetic and presents transcomplex arithmetic, and designs a pipelined dataflow machines with a large number of cores that can complete the execution of multiple in-line programs each clock tick. Expand

A FÍSICA NEWTONIANA TRANSREAL OPERA EM SINGULARIDADES

- Mathematics
- 2015

Sir Isaac Newton, writing in Latin, defined his celebrated laws of motion verbally. When the laws of motion are read as relating to his arithmetic (the Arithmetica Universalis) and his calculus (the… Expand

Transvector Algebra and Analysis Operate at Singularities

- Mathematics
- 2014

We show that transcomplex numbers can be modelled by real, homogeneous co-ordinates with arbitrary Cartesian elements and a non-negative homogeneous element. Hence we develop transvectors as tuples… Expand

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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… Expand

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