{"id":362,"date":"2016-06-01T20:49:49","date_gmt":"2016-06-01T20:49:49","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/?post_type=chapter&p=362"},"modified":"2019-08-06T17:21:21","modified_gmt":"2019-08-06T17:21:21","slug":"outcome-solve-one-step-linear-equations-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/chapter\/outcome-solve-one-step-linear-equations-2\/","title":{"raw":"Introduction to Classifying and Defining Properties of Real Numbers","rendered":"Introduction to Classifying and Defining Properties of Real Numbers"},"content":{"raw":"The real numbers can be divided into three subsets: negative real numbers, zero, and positive real numbers. Each subset includes fractions, decimals, and irrational numbers according to their algebraic sign (+ or \u2013). In this section we will further define real numbers and use their properties to solve linear equations and inequalities.\r\n\r\nThe classes of numbers we will explore include:\r\n

Natural numbers<\/span><\/h3>\r\nThe most familiar numbers are the natural numbers (sometimes called counting numbers): [latex]1, 2, 3[\/latex], and so on. The mathematical symbol for the set of all natural numbers is written as [latex]\\mathbb{N}[\/latex].\r\n

Whole numbers<\/span><\/h3>\r\nThe set of whole numbers includes all natural numbers as well as\u00a0 [latex]0[\/latex].\r\n

Integers<\/span><\/h3>\r\nWhen the set of negative numbers is combined with the set of natural numbers (including\u00a00), the result is defined as the set of integers,\u00a0[latex]\\mathbb{Z}[\/latex].\r\n

Rational numbers<\/span><\/h3>\r\n
A rational number,\u00a0[latex]\\mathbb{Q}[\/latex], is a number that can be expressed as a fraction with an integer numerator and a positive integer denominator.<\/div>\r\n

Real numbers<\/h3>\r\n
The real numbers\u00a0include all the measuring numbers. The symbol for the real numbers is [latex]\\mathbb{R}[\/latex]. Real numbers are usually represented by using decimal numerals.<\/div>","rendered":"

The real numbers can be divided into three subsets: negative real numbers, zero, and positive real numbers. Each subset includes fractions, decimals, and irrational numbers according to their algebraic sign (+ or \u2013). In this section we will further define real numbers and use their properties to solve linear equations and inequalities.<\/p>\n

The classes of numbers we will explore include:<\/p>\n

Natural numbers<\/span><\/h3>\n

The most familiar numbers are the natural numbers (sometimes called counting numbers): [latex]1, 2, 3[\/latex], and so on. The mathematical symbol for the set of all natural numbers is written as [latex]\\mathbb{N}[\/latex].<\/p>\n

Whole numbers<\/span><\/h3>\n

The set of whole numbers includes all natural numbers as well as\u00a0 [latex]0[\/latex].<\/p>\n

Integers<\/span><\/h3>\n

When the set of negative numbers is combined with the set of natural numbers (including\u00a00), the result is defined as the set of integers,\u00a0[latex]\\mathbb{Z}[\/latex].<\/p>\n

Rational numbers<\/span><\/h3>\n
A rational number,\u00a0[latex]\\mathbb{Q}[\/latex], is a number that can be expressed as a fraction with an integer numerator and a positive integer denominator.<\/div>\n

Real numbers<\/h3>\n
The real numbers\u00a0include all the measuring numbers. The symbol for the real numbers is [latex]\\mathbb{R}[\/latex]. Real numbers are usually represented by using decimal numerals.<\/div>\n\n\t\t\t
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