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Classification of Numbers

Definitions:

Natural Numbers: (1) The counting numbers.  (2) Members of the set{1,2,3,4,...}

Whole Numbers: (1) The natural numbers plus the number zero.  (2) Members of the set {0,1,2,3,4,...}.

Integers: (1) The set of numbers made up of the whole numbers plus the opposites of the natural numbers.  (2) Members of the set {...,-3,-2,-1,0,1,2,3,...}.

Rational Numbers: (1) The set of numbers which may be represented as an integer divided by a nonzero integer.  (2) Any number that can be expressed in the form a/b, where a is an integer and b is an integer other than zero.

Irrational Numbers:  (1) The set of non-terminating, non-repeating decimal numbers.  (2) The set of real numbers that are not also members of the rational number set.

Real Numbers:  The set of numbers made up of the set of rational numbers and the set of irrational numbers.  

Note: each real number is paired with exactly one point on a number line; and, each point on a number line is paired with exactly one real number.  Thus, the graphs of all real numbers make up the entire number line.

Lesson 1.1: Real Numbers -- Lesson Summary

? Of ?

Natural Numbers

{1, 2, 3, 4, 5, ...}

Zero

{0}

{1, 2, 3, 4, 5, ...}

Whole Numbers

{0, 1, 2, 3, 4, ...}

Opposites of Natural Numbers

{... ,-4, -3, -2, -1}