A number is a mathematical object used to count, measure, and label. It is a fundamental concept that forms the basis of all mathematics. It can be described in many ways, but the most basic are the natural numbers 1, 2, 3, and so forth. They can be represented in language with number words, such as "six" and "seven."
The set of computable numbers is a subset of the real numbers that are amenable to algorithmic analysis. A number is said to be computable if there exists an algorithm that, given the first digits of its decimal representation, will produce the remainders for all possible digits. The set of computable numbers is complete, so every positive number can be found in this set.
In general, the term number is used to refer to any countable or uncountable entity that has a value and can be manipulated with the operations of addition, subtraction, multiplication, division, and sometimes inverses. However, there are a number of other objects that have the same properties as numbers and that are considered to be part of the same category of mathematical objects: for example, functions, p-adic numbers, algebraic numbers, and complex numbers.
Early civilizations developed different methods to show quantities. They started by counting on their fingers or using tally marks to mark the number of objects or actions they had done. Later they learned to use a set of symbols that made it easier to show larger numbers. In the seventh century, the Hindu-Arabic numeral system was perfected in India and became the most widely used way of representing numbers to this day.
The term "integer" is generally used to refer to a Number_i that is greater than zero, but it can also be used to describe a set of numbers. The integers can be sorted in various ways to find patterns or trends. The median, mean, and mode are measures of central tendency in a group of numbers.
Among the most important numbers in mathematics are fractions, ratios, and percentages. A fraction is a representation of a whole number as a share of the total amount. It can be written in any of the following forms:
A ratio is a relationship between two numbers that is expressed as a decimal or a percent. Percentages are usually denoted by the symbol % after the number and can be calculated by dividing the numerator and denominator of a number by 100. The percentage can then be applied to a number of objects or actions. For example, a percentage of the total cost of a project is equal to the ratio of the number of dollars spent divided by the total amount of money. The percentage is then multiplied by the original amount to get the result of the total expense. This number can then be compared to the original amount of money and the results of the other expenses to determine which one is more cost effective.
