Editing Division by zero (section)

=== In proof assistants ===

Many [[proof assistant]]s, such as [[Rocq (software)|Rocq]] (previously known as ''Coq'') and [[Lean (proof assistant)|Lean]], define 1/0 = 0. This is due to the requirement that all functions are [[Total functional programming|total]]. Such a definition does not create contradictions, as further manipulations (such as [[cancelling out]]) still require that the divisor is non-zero.<ref>{{cite conference |mode=cs2 |last1=Tanter |first1=Éric |last2=Tabareau |first2=Nicolas |title=Gradual certified programming in coq |year=2015 |publisher=Association for Computing Machinery |book-title=DLS 2015: Proceedings of the 11th Symposium on Dynamic Languages |doi=10.1145/2816707.2816710 |quote=The standard division function on natural numbers in Coq, div, is total and pure, but incorrect: when the divisor is 0, the result is 0.|arxiv=1506.04205 }}</ref><ref>{{citation |last1=Buzzard |first1=Kevin |title=Division by zero in type theory: a FAQ |type=Blog |url=https://xenaproject.wordpress.com/2020/07/05/division-by-zero-in-type-theory-a-faq/ |website=Xena Project |date=5 July 2020 |access-date=2024-01-21}}</ref>