In mathematics there are various types of numbers. They are defined by specific use and properties: counting, measuring, representing quantities, etc.
Common number types:
Definition: [A number is real if it can be represented EITHER on a number line OR by an infinite decimal expansion.]
Real numbers can be used to measure a continuous one-dimensional quantity, for example numbers related to the measurement of:
These numbers present themselves as continuous variables, meaning that they can take on any value within a given range. Between any two points there are infinite possible values. For example, room temperature at any given time can have infinite fractional value.
A variable respresents an unspecified value, that can hold different types of information (data). It is used to represent variable, or alterable, or yet to be defined, data, part of an operation or function that allows, or prepares for input.
The integer is a number that is non-fractional and can be either negative or positive.
A natural number is a positive integer used (primarily) for counting (cardinal) and orderning (ordinal).
Natural numbers are also real numbers, which is a wider category. Natural numbers are defined more narrowly. They begin with 1 and can count up without end. Negative numbers, fractions and decimals or not natural numbers.
A whole number is a positive integer used (primarily) for counting (cardinal), orderning (ordinal) and for representing the absence of quantity (zero / o).
Whole numbers are also real numbers, which is a wider category. Whole numbers are, like natural numbers defined more narrowly. They overlap with natural numbers, the difference being that they begin with 0. But just like natural numbers they can count up without end. Negative numbers, fractions and decimals or not whole numbers.
A fractional number is an equal part of a divided whole. It is written as two whole numbers divided by a line. The number that exist above or to the left from the line is called the numerator. This number shows how many parts are counted from the total amount of parts in which the whole number has been divided. The number below or to the right from the line is called the denominator. This number shows the total number of equal parts by which the whole number has been divided. For example: the expression 2/5 means that two parts are counted out of a total of five equal parts.
A rational number is a number that can be written as a fraction, with the denominator not being zero. Examples: 2/4, -6/8, and 4 (= 4/1).
An irrational number is any real number that is not also a rational number. Irrational numbers can not be written as a fraction. Great example is the number Pi.
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