@article{Bergstra_2022, title={Prospective, Retrospective, and Formal Division:: a contribution to philosophical arithmetic}, url={https://transmathematica.org/index.php/journal/article/view/71}, DOI={10.36285/tm.71}, abstractNote={<p>Division by zero is a controversial theme.<span class="Apple-converted-space"> </span>Why is division by zero a relevant issue and how can this issue be<span class="Apple-converted-space">  </span>addressed from different perspectives? Fracterm is used as an abbreviation for fractional expression.<span class="Apple-converted-space"> </span>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,<span class="Apple-converted-space"> </span>computer programming gives rise to prospective occurrences, and so does automated proof checking.<span class="Apple-converted-space"> </span>The use of division in an axiom system<span class="Apple-converted-space"> </span>may indicate the presence of formal occurrences of division symbols.</p>}, journal={Transmathematica}, author={Bergstra, Jan Aldert}, year={2022}, month={Oct.} }