https://transmathematica.org/index.php/journal <p>Publishes articles and digital works in the sciences, humanities and arts of total (exception free) systems and new or adventurous mathematics.</p> Dr James Anderson, 88 Lower Henley Road, Caversham, Reading, England, RG4 5LE. https://en.wikipedia.org/wiki/James_A._D._W._Anderson en-US Transmathematica 2632-9212 <p>Authors retain copyright and, if appropriate, performance rights but licence the journal to publish submissions. The lead author confirms that the submission is bound by&nbsp;the <a href="http://creativecommons.org/licenses/by-sa/4.0">CC Attributtion Share Alike 4.0</a>&nbsp;licence.</p> https://transmathematica.org/index.php/journal/article/view/97 <p>A common meadow is an enrichment of a field with a division operator and an error value to make division total. A signed common meadow enriches a common meadow with a sign function that can be equationally axiomatised; the sign function can simulate an ordering on the underlying field but is not limited to orderings. In particular, of mathematical interest are the weakly signed common meadows. The prime example of a weakly signed common meadow is an expansion of a common meadow of complex numbers with a weak sign function. We show that all common meadows may be enlarged to a weakly signed common meadow. A special case is the 4-signed common meadows, which are precisely the enlargements of ordered fields. To illustrate the equational calculus for signed common meadows, we use it as a foundation for building a probability calculus and derive some classical formulae.</p> Jan Aldert Bergstra John V Tucker Copyright (c) 2024 Jan Aldert Bergstra, John V Tucker http://creativecommons.org/licenses/by-sa/4.0 2024-06-14 2024-06-14 10.36285/tm.97