Fracpairs and Quantitative Mereology
DOI:
https://doi.org/10.36285/tm.129Abstract
Fracpairs may be taken for a basic entity in arithmetic. A fracpair is the input pair for a division. A fracpair may also be called a ratio. Fracpairs can be built on any arithmetic, starting with naturals or integers. Fracpairs are taken as elements of an additional sort, for which additional operations may be introduced in a stepwise manner. These operations are mainly implementations of well-known from Elementary Arithmetic with Division (EAwD), for which however a ramification of different implementations arises due to the low level of abstraction of inputs. A fundamental interpretation of a fracpair is that it selects, or describes a selection, a number of parts of an entity which has been split in a number of comparable parts. The paper proposes various options for formalizing the split and select interpretations of fracpairs.
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