Editing Division by zero (section)

==Early attempts==
The ''[[Brāhmasphuṭasiddhānta]]'' of [[Brahmagupta]] (c. 598–668) is the earliest text to treat [[0|zero]] as a number in its own right and to define operations involving zero.<ref name="Kaplan">{{citation |last=Kaplan |first=Robert |title=The Nothing That Is: A Natural History of Zero |url=https://archive.org/details/nothingthatisnat00kapl |url-access=registration |publisher=Oxford University Press |year=1999 |location=New York |pages=[https://archive.org/details/nothingthatisnat00kapl/page/68 68–75] |isbn=978-0-19-514237-2}}</ref> According to Brahmagupta,

<blockquote>A positive or negative number when divided by zero is a fraction with the zero as denominator. Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero.</blockquote>

In 830, [[Mahāvīra (mathematician)|Mahāvīra]] unsuccessfully tried to correct the mistake Brahmagupta made in his book ''[[Gaṇita-sāra-saṅgraha|Ganita Sara Samgraha]]'': "A number remains unchanged when divided by zero."<ref name="Kaplan"/>

[[Bhāskara II]]'s ''[[Līlāvatī]]'' (12th century) proposed that division by zero results in an infinite quantity,<ref>{{citation |last=Roy |first=Rahul |journal=Resonance |volume=8 |number=1 |date=January 2003 |title=Babylonian Pythagoras' Theorem, the Early History of Zero and a Polemic on the Study of the History of Science |pages=30–40 |url=https://www.ias.ac.in/describe/article/reso/008/01/0030-0040 |doi=10.1007/BF02834448 }}</ref>

<blockquote>A quantity divided by zero becomes a fraction the denominator of which is zero. This fraction is termed an infinite quantity. In this quantity consisting of that which has zero for its divisor, there is no alteration, though many may be inserted or extracted; as no change takes place in the infinite and immutable God when worlds are created or destroyed, though numerous orders of beings are absorbed or put forth.</blockquote>

Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to <math display="inline">\tfrac{a}{0}</math> is contained in [[Anglo-Irish people|Anglo-Irish]] philosopher [[George Berkeley]]'s criticism of [[Calculus#Limits and infinitesimals|infinitesimal calculus]] in 1734 in ''[[The Analyst]]'' ("ghosts of departed quantities").<ref>{{citation
 | last = Cajori | first = Florian | author-link = Florian Cajori
 | journal = The Mathematics Teacher
 | volume = 22 | issue = 6 | jstor = 27951153
 | pages = 366–368
 | title = Absurdities due to division by zero: An historical note| year = 1929 | doi = 10.5951/MT.22.6.0366 }}.</ref>