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Real Numbers

Main Concept

The real numbers are numbers representing quantities that can vary on a continuous scale. They include the natural numbers, whole numbers, integers, rational numbers and irrational numbers. The set of real numbers is denoted by ℝ.



Natural numbers: the counting numbers, beginning with 1, represented by ℕ.


Whole numbers: the natural numbers and 0


Integers: the natural numbers, their negative counterparts, and 0, represented by ℤ.


Rational numbers: numbers that can be represented as a ratio of integers; ab, where a and b are integers and b0. The decimal representation of a rational number either terminates or has a repeating pattern. The set of rationals is represented by ℚ.


Irrational numbers: numbers that cannot be represented as a ratio of integers. The decimal form of a rational number is non-repeating and non-terminating.


Some of the above sets of numbers are subsets, or more specific groups, of other sets. For example, the natural numbers are a subset of the integers; that is, all natural numbers are integers, specifically those integers greater than 0. All integers, in turn, are rational numbers. Given an integer a, it can be represented as the ratio a1. On the other hand, the sets of rational and irrational numbers are complements: a number can be either rational or irrational, but not both.


Use the check boxes to see which of the real numbers below are of the given type.





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