Manifesto for Transreal Arithmetic

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Manifesto for Transreal Arithmetic

• Manifesto for Computing
• Transreal arithmetic is a total arithmetic. This
  means that every arithmetical operation can be
  applied to any numbers and the result is a
  number.
• Transreal arithmetic defines division by
• In particular, this defines division by zero.
• Transreal arithmetic reduces numbers with a zero
  denominator to least terms like this. Here k is
  positive
• Transreal arithmetic defines addition by
• Except that
• It has been proved that transreal arithmetic is
  self consistent and that it contains real
  arithmetic as a subset. This means that transreal
  arithmetic computes the same results as real
  arithmetic, wherever real arithmetic applies, but
  it also computes consistent results where real
  arithmetic does not apply.
• Transreal arithmetic generalises trigonometry,
  calculus and metric spaces so all practical
  computations are made total.

Manifesto for Education Primary schools
throughout the world teach But this is false,
in real arithmetic, because it allows division by
zero. Secondary schools and universities
throughout the world teach Where a is
positive and finite. But this is false, as this
counter example shows These falsehoods arise
because teachers do not teach the guarding
clauses that are needed to exclude the
exceptional cases where real arithmetic does not
apply. Manifesto conduct research to see if it
is more effective to continue teaching arithmetic
via falsehoods or whether it is better to teach a
total arithmetic. Manifesto for Physics
Physical equations that involve division by
zero are said to have poles or singularities.
Real arithmetic breaks down in these cases, but
it is sometimes possible to get useful
information by examining the locations where
poles and singularities occur. If the physical
universe operates according to real arithmetic,
how does it know it should break down when
dividing by zero, and how does it know what to do
in these cases? If physical equations are
written in transreal arithmetic, and its
generalisations, then thy never break down. The
universe can continue to work, even if it
divides by zero. Manifesto conduct research to
see if it is useful to re-work physical equations
in transreal arithmetic and its generalisations.

• Contact information
• School of Systems Engineering, University of
  Reading, Whiteknights, Reading, England, RG6 6AY
• Email j.anderson_at_reading.ac.uk
• www.reading.ac.uk/sse/about/Staff/j-anderson.asp