Introduction: Classify and Define Properties of Real Numbers
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 –). In this section we will further define real numbers and use their properties to solve linear equations and inequalities. The classes of numbers we will explore include:Natural numbers
The most familiar numbers are the natural numbers (sometimes called whole numbers or 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], and sometimes [latex]\mathbb{N_0}[/latex] or [latex]\mathbb{N_1}[/latex] when it is necessary to indicate whether the set should start with [latex]0[/latex] or [latex]1[/latex], respectively.Integers
When the set of negative numbers is combined with the set of natural numbers (including 0), the result is defined as the set of integers, [latex]\mathbb{Z}[/latex]Rational numbers
A rational number is a number that can be expressed as a fraction with an integer numerator and a positive integer denominator.
Real numbers
The real numbers include all the measuring numbers. The symbol for the real numbers is [latex]\mathbb{R}[/latex]. Real numbers are usually represented by using decimal numerals.
The specific things you’ll learn in this section include:
- Classify a real number as a natural, whole, integer, rational, or irrational number
- Define and use the commutative property of addition and multiplication
- Define and use the associative property of addition and multiplication
- Define and use the distributive property
- Define and use the identity property of addition and multiplication
- Define and use the inverse property of addition and multiplication
- Define and identify constants in an algebraic expression
- Evaluate algebraic expressions for different values
The learning activities for this outcome include
- Read: Classify real numbers
- Self-Check: Classify real numbers
- Read: Use properties of real numbers
- Self-Check: Use properties of real numbers
- Read: Evaluate algebraic expressions
- Self-Check: Evaluate algebraic expressions
Licenses & Attributions
CC licensed content, Original
- Revision and Adaptation. Provided by: Lumen Learning License: CC BY: Attribution.
CC licensed content, Shared previously
- Unit 10: Solving Equations and Inequalities, from Developmental Math: An Open Program. Provided by: Monterey Institute of Technology and Education Located at: https://www.nroc.org/. License: CC BY: Attribution.
