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In mathematics, Da dat Hamilton King George Chorus Mug the notion of number has been extended over the centuries to include 0, negative numbers rational numbers such as , real numbers such as √2 and π, and complex numbers, which extend the real numbers with a square root of −1 Calculations with numbers are done with arithmetical operations, the most familiar being addition, subtraction, multiplication, division, and exponentiation. Their study or usage is called arithmetic. The same term may also refer to number theory, the study of the properties of numbers. The use of 0 as a number should be distinguished from its use as a placeholder numeral in place-value systems. Many ancient texts used 0. Babylonian and Egyptian texts used it. Egyptians used the word nfr to denote zero balance in double entry accounting. Indian texts used a Sanskrit word Shunye or shunya to refer to the concept of void. In mathematics texts this word often refers to the number zero. In a similar vein, Pāṇini used the null operator in the Ashtadhyayi, an early example of an algebraic grammar for the Sanskrit language
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There are other uses of zero before Brahmagupta, though the documentation is not as complete as it is in the Brāhmasphuṭasiddhānta. Records show that the Ancient Greeks seemed unsure about the status of 0 as a number: they asked themselves “how can ‘nothing’ be something?” leading to interesting philosophical and, by the Medieval period, religious arguments about the nature and existence of 0 and the vacuum. The paradoxes of Zeno of Elea depend in part on the uncertain interpretation of 0. The late Olmec people of south-central Mexico began to use a symbol for zero, a shell glyph, in the New World, possibly by the 4th century BC but certainly by 40 BC, which became an integral part of Maya numerals and the Maya calendar. Mayan arithmetic used base 4 and base 5 written as base 20. Sanchez in 1961 reported a base 4, base 5 “finger” abacus.
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