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The Story Of One

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The Story Of One

The natural numbers had their origins in the words used to count things, beginning with the number 1.

The first major advance in abstraction was the use of numerals to represent numbers. This allowed systems to be developed for recording large numbers. The Babylonians, for example, developed a powerful place-value system based essentially on the numerals for 1 and 10. The ancient Egyptians had a system of numerals with distinct hieroglyphs for 1, 10, and all the powers of 10 up to one million. A stone carving from Karnak, dating from around 1500 BC and now at the Louvre in Paris, depicts 276 as 2 hundreds, 7 tens, and 6 ones; and similarly for the number 4,622.

A much later advance in abstraction was the development of the idea of zero as a number with its own numeral. A zero digit had been used in place-value notation as early as 700 BC by the Babylonians but they omitted it when it would have been the last symbol in the number. The Olmec and Maya civilization used zero developed independently as a separate number as early as 1st century BC, but this usage did not spread beyond Mesoamerica. The concept as used in modern times originated with the Indian mathematician Brahmagupta in 628. Nevertheless, medieval computers (e.g. people who calculated the date of Easter), beginning with Dionysius Exiguus in 525, used zero as a number without using a Roman numeral to write it. Instead nullus, the Latin word for "nothing", was employed.

The first systematic study of numbers as abstractions (that is, as abstract entities) is usually credited to the Greek philosophers Pythagoras and Archimedes. Note that many Greek mathematicians did not consider 1 to be "a number", so to them 2 was the smallest number.

Independent studies also occurred at around the same time in India, China, and Mesoamerica.

Several set-theoretical definitions of natural numbers were developed in the 19th century. With these definitions it was convenient to include 0 (corresponding to the empty set) as a natural number. Including 0 is now the common convention among set theorists, logicians, and computer scientists. Many other mathematicians also include 0, although some have kept the older tradition and take 1 to be the first natural number. Sometimes the set of natural numbers with 0 included is called the set of whole numbers or counting numbers.

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