Question

a) Are all rational numbers real numbers? b) Are all irrational numbers real numbers?

    a) Are all rational numbers real numbers?
b) Are all irrational numbers real numbers?

Intermediate Algebra for College Students

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 4, Problem 106

Instant Answer

Solved by Expert Mukesh Devi

03/07/2024

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Real numbers include all numbers that can be represented on the number line, which includes all rational numbers. Show more…

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a) Are all rational numbers real numbers? b) Are all irrational numbers real numbers?

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Key Concepts

Rational Numbers

Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. They include numbers that can be written in fractional form, and they form one of the two main subsets of real numbers discussed in the context of number theory and arithmetic.

Irrational Numbers

Irrational numbers are numbers that cannot be expressed as a simple fraction of two integers. Their decimal representations are non-terminating and non-repeating, and they occupy the complementary subset of the real numbers alongside rational numbers.

Real Numbers

Real numbers consist of all the numbers that can be found on the number line, including both rational and irrational numbers. They form a complete set in the sense that every point on the number line corresponds to a unique real number, which is a foundational concept in mathematics and calculus.

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