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HomeHomework HelpmathematicsFundamental Properties of Real Numbers

Fundamental Properties of Real Numbers

The fundamental properties of real numbers include the associative, commutative, and distributive properties, which govern the behavior of addition and multiplication, allowing for the manipulation of numerical expressions.

beginner
2 hours
Mathematics
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Overview

Real numbers are a fundamental concept in mathematics, encompassing both rational and irrational numbers. They are essential for various mathematical operations and real-world applications, such as finance and engineering. Understanding the properties of real numbers, including closure, associative,...

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Key Terms

Real Numbers
Numbers that include both rational and irrational numbers.

Example: 3, -1.5, √2 are all real numbers.

Rational Numbers
Numbers that can be expressed as a fraction of two integers.

Example: 1/2, 3, -4 are rational numbers.

Irrational Numbers
Numbers that cannot be expressed as a simple fraction.

Example: π and √2 are irrational numbers.

Closure Property
The result of an operation on two numbers in a set is also in that set.

Example: Adding two integers results in an integer.

Associative Property
The way numbers are grouped does not change their sum or product.

Example: (2 + 3) + 4 = 2 + (3 + 4).

Commutative Property
The order of numbers does not affect their sum or product.

Example: 3 + 5 = 5 + 3.

Related Topics

Complex Numbers
Complex numbers extend real numbers to include imaginary units, useful in advanced mathematics.
intermediate
Algebraic Expressions
Algebraic expressions involve variables and constants, building on the properties of real numbers.
intermediate
Functions and Graphs
Functions use real numbers to map inputs to outputs, essential for understanding relationships in math.
intermediate

Key Concepts

Closure PropertyAssociative PropertyCommutative PropertyDistributive Property