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Real Numbers

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.

Natural Numbers

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

Zero

{0}

Whole Numbers

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

Opposites of Natural Numbers

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

Integers

{... -2, -1, 0, 1, 2, ...}

Non-Integral

Rationals

Ex: -5.7, -¼, ½, 3⅞

Irrational Numbers

{... -2, -1, 0, 1, 2, ...}

Rational Numbers

Ex: -2, -¾, 0, 4.6, 8⅞

CLASSIFICATION OF REAL NUMBERS - CONTINUED

8. I suspect that you have already figured out that if we combine the sets of Rational and Irrational Numbers we create the set of Real 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.

• Just so you know, our number system is still not complete since we still haven’t talked about Imaginary and Complex Numbers. We will save those discussions for Integrated Algebra 2.

Lesson 1.1: Real Numbers -- The Real Numbers

9 Of 10

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