Natural numbers are represented by 1, 2, 3, and so on, and include 0 if defined as non-negative integers. They are whole numbers used for counting or ordering, and are only positive. Zero was created by the Maya and Olmec civilizations, but the Indian usage was adopted by civilizations like the Greeks. Natural numbers are used in mathematical applications such as set theory and number theory, and are taught to children from a young age. Whole numbers and negative numbers are introduced later.
A natural number, which can also be called a count number, is represented by the digits 1, 2, 3 up to infinity. The number 0 is included if natural numbers are defined as non-negative integers, but not if they are defined as positive integers only. In mathematics, there must be an infinite number of natural digits, since every natural number is defined in part by a number following it. These numbers are also whole numbers, not fractions or decimals, and can be used for counting or ordering.
The main distinction between a natural number and an integer is that natural numbers, with the exception of zero, are only positive. There is no number less than zero, and a natural number cannot be followed by zero, as is the case with -1.0. Essentially this defines natural numbers as anything zero or greater that is integer and not fractional. Zero is generally considered to be the only non-positive natural number.
The concept of zero evolved long after civilizations started counting numbers. The earliest records of counting numbers from 1 to 10 date back over 4,000 years, when the Babylonians used the use of a specific written code to indicate location. The Egyptians wrote hieroglyphics for each digit, but it wasn’t until around 1000 BC that the concept of zero was created by the Maya and Olmec civilizations.
Although the Olmec and Mayan groups show the first records of the use of zero, the concept of zero also developed in India, in the 7th century BC. It was the Indian usage, rather than the Mesoamerican usage, that was adopted by civilizations such as the Greeks.
There are many ways that the natural numbers can be used in mathematical applications. They can narrow down the problems by suggesting that the answer must be a natural number. They are also studied in specific applications in set theory, mathematics that evaluates sets of things. Number theory can evaluate natural numbers as part of the set of integers or independently to see whether they behave in certain ways or exhibit certain properties.
Perhaps one of the broader uses of the natural numbers comes very “naturally” to us. As young people we learn to count from 0 onwards. Even young children can easily start learning the difference between one and two, or explain how old they are. This study continues as children enter school and learn to manipulate natural numbers, such as multiplying, dividing, adding and subtracting them. Only after learning the concept of natural numbers is the concept of whole numbers introduced, and the possibility of negative numbers, which may be confusing to some children at first, is usually learned at the earliest in fourth or fifth grade.
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