The number that represents nothing, and also the placeholder that makes positional numeral systems work. A placeholder symbol for an empty position appears in Babylonian and Mayan numeral systems centuries earlier, but treating zero as a genuine NUMBER, one that can be added, subtracted and multiplied by the ordinary rules, is generally credited to Indian mathematics; the seventh century Indian mathematician Brahmagupta gave the first known explicit rules for arithmetic with zero (and division by it) in his 628 CE work Brahmasphutasiddhanta. The zero and the whole Hindu-Arabic positional system carrying it reached medieval Europe substantially through Arabic mathematics, Al-Khwarizmi's work prominent among the channels, and through Fibonacci's 1202 Liber Abaci.
Facts
Origin YearDates Brahmagupta's first known explicit arithmetic rules for zero; the placeholder use in positional notation is considerably older and less precisely datable. FAQs
Is zero a natural number?
Depends on the convention: some traditions start the natural numbers at 0, others at 1.
It depends which convention a text uses, and both are standard. Many number theory and classical texts start the natural numbers at 1, treating zero as a separate case added on. Set theory and most modern computer science texts start at 0, since 0 is the size of the empty set and the natural starting point for counting from nothing. Neither convention is wrong; a careful text states which one it means.
Connections
Associated With
Al-Khwarizmi's work was a major channel carrying the Hindu-Arabic numeral system, zero included, into the Islamic world and, through Latin translation, into medieval Europe.
Source MacTutor History of Mathematics Archive
Attributed To
Source Wikipedia: 0 (Number)
In Branch
Source MacTutor History of Mathematics Archive
Sources
1. MacTutor History of Mathematics Archive
University of St Andrews, School of Mathematics and Statistics
Wikipedia: 0 (Number)
Wikimedia FoundationLead section
Historically, ought, aught (), and cipher have also been used.
Attributed To: Bhāskara II, Lead
Bhāskara II's 12th century treatise Līlāvatī instead proposed that division by zero results in an infinite quantity
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