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Explain the relationships and differences among real numbers, rational numbers, and irrational numbers.
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The relationships and differences among real numbers, rational numbers, and irrational numbers.
Answer to Problem 1CCE
Solution:
Relationship among real numbers, rational numbers, and irrational numbers is that the sets of rational numbers and irrational numbers are subsets of set of real numbers.
Difference between rational and irrational number is that the rational number can be written as
Explanation of Solution
Given information:
Set of real numbers, rational numbers, and irrational numbers
Explanation:
Rational numbers are the numbers which can be written as
Irrational numbers are the numbers which cannot be written as a ratio of two integers and have non-repeating and non-terminating decimals. For example,
The rational as well as irrational numbers can be converted to decimals and can be shown on the number line as shown below,
So, rational and irrational numbers are subsets of real numbers.
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Calculus & Its Applications (14th Edition)
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