Prospective, Retrospective, and Formal Division

Abstract

Division by zero is a controversial theme. Why is division by zero a relevant issue and how can this issue be addressed from different perspectives? Fracterm is used as an abbreviation for fractional expression. Three types of occurrence of the division symbol in a fracterm are distinguished: prospective occurrence, retrospective occurrence, and formal occurrence. Mathematics mostly features retrospective occurrences of division, computer programming gives rise to prospective occurrences, and so does automated proof checking. The use of division in an axiom system may indicate the presence of formal occurrences of division symbols.

Transreal Foundation for Floating-Point Arithmetic

“…Also in this year a review of approaches to division by zero [52] discussed fracterm calculus and the transreals. A paper on totalising partial algebras [53] discussed the transreals, among other approaches to division by zero.…”