Chapter 1 Summary

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Section 1.3 Chapter 1 Summary

Subsection Important Definitions

Subsection Important Number Systems and Their Properties

The natural numbers, \(\N\text{;}\) the integers, \(\Z\text{;}\) the rational numbers, \(\Q\) and the real numbers, \(\R\text{.}\) See Closure Properties of Number Systems

Closure Properites of the Number Systems.

Number System	Closed Under
Natural Numbers, \(\N\)	addition and multiplication
Integers, \(\Z\)	addition, subtraction, and multiplication
Rational Numbers, \(\Q\)	addition, subtraction, multiplication, and division by nonzero rational numbers
Real Numbers, \(\R\)	addition, subtraction, multiplication, and division by nonzero real numbers

Inverse, communtative, associative, and distributive properties of the real numbers. See Properties of Number Systems.

Subsection Important Theorems and Results