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Transreal Limits Expose Category Errors in IEEE 754 Floating-Point Arithmetic and in Mathematics

- James Anderson, T. Reis
- Mathematics
- 6 August 2014

The IEEE 754 standard for
oating-point arithmetic is widely used in
computing. It is based on real arithmetic and is made total by adding both
a positive and a negative infinity, a negative zero,… Expand

Construction of the Transreal Numbers and Algebraic Transfields

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

Construction of the transcomplex numbersfrom the complex numbers

- T. Reis, James Anderson
- Mathematics
- 22 October 2014

A geometrical construction of the transcomplex numbers was given
elsewhere. Here we simplify the transcomplex plane and construct the
set of transcomplex numbers from the set of complex numbers.… Expand

Transdifferential and transintegral calculus

- T. Reis, James Anderson
- Mathematics
- 22 October 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

The role of cortico-striatal circuits in social hierarchies

- T. Reis
- Psychology
- 22 September 2017

Validação de um escore para predição de eventos hemorrágicos em síndromes coronarianas agudas

- Luis Cláudio Lemos Correia, Saulo Merelles, +5 authors José Péricles Esteves
- Medicine
- 1 October 2010

FUNDAMENTO: Sangramento e uma complicacao grave em pacientes tratados para sindromes coronarianas agudas (SCA) com antitromboticos e terapias invasivas. Consequentemente, o beneficio dessas terapias… Expand

Integral on transcomplex numbers

- T. Reis, James Anderson
- Mathematics
- 2019

The usual complex integral is defined in terms of complex numbers in Cartesian form but transcomplex numbers are defined in polar form and almost all transcomplex numbers, with infinite magnitude,… Expand

Derivations of Evolution Algebras associated to graphs over a field of any characteristic

- T. Reis, Paula Cadavid
- Mathematics
- 21 June 2020

The space of derivations of finite dimensional evolution algebras associated to graphs over a field with characteristic zero has been completely characterized in the literature. In this work we… Expand

Transreal proof of the existence of universal possible worlds

- Walter Gomide, T. Reis, James Anderson
- Mathematics
- 6 January 2015

Transreal arithmetic is total, in the sense that the fundamental operations of addition, subtraction, multiplication and division can be applied to any
transreal numbers with the result being a… Expand

Transcomplex Numbers : Properties , Topology and Functions

- T. Reis, James Anderson
- 2017

We derive the properties of transcomplex arithmetic from the usual definition of transcomplex numbers as a fraction of complex numbers, whose denominator may be zero. This is equivalent to giving an… Expand

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