Counting is the basis of arithmetic. Addition has its beginnings in counting. If one wants to add 2 apples to 3 apples, one can put them all together and count them. The sum is 5 apples. Subtraction is defined as the opposite of addition - take some away and see how many are left. Multiplication is defined as repeated addition. 3×4 means multiply 3 by itself 4 times: 3+3+3+3. Division is defined as the opposite of multiplication.
Counting has it origins in people needing to communicate a quantity. For examples, a village leader might know how many ears of corn are needed to feed the village through the winter. As the harvest progresses, the leader can count the ears of corn put into the grainery to see if they will have enough.
But counting is not enough. One might want to keep the quantity and tell someone else what the quantity is. This is where numeration comes in. Numeration is how a quantity is recorded or spoken about. Many different ways have been invented to record quantities. Some of the more primitive forms of numerals were notches on a stick or bone, or knots in a rope. Later, people began to use symbols to represent quantity. The ancient Babylonians used various symbols to represent numbers that were written on clay tablets.
The numbers we use today originated in India. Hindu accountants needed to write down numbers, so they used symbols for the digits 0 through 9, then used place value for larger numbers, like we do today. These symbols were adopted by Arabian scholars. Eventually, these symbols were adopted, in a changed form, in Europe, then throughout the world.
So far, this article has discussed counting using whole numbers. People also need to count parts of things, such as half a bushel of wheat. The next step in counting was fractions. Fractions were used for several thousands of years. Some ancient mathematicians believed that any number could be shown with a whole number or a fraction. Later, the decimal separator was invented. This allowed people to count very small things, such as the thickness of a molecule of oil. As mathematicians studied the nature of numbers, they eventually proved that fractions of whole numbers can not represent all real numbers.
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