Tell which set or sets the number belongs to: natural numbers, whole numbers, integers, ra...

Tell which set or sets the number belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. See Example 5.

EXAMPLE 5 Given the set , list the numbers in this set that belong to the set of:

a. Natural numbers

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b. Whole numbers

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c. Integers

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d. Rational numbers

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e. Irrational numbers

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f. Real numbers

Solution

a. The natural numbers are 11 and 112.

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b. The whole numbers are 0,11, and 112.

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c. The integers are −3, −2, 0,11, and 112.

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d. Recall that integers are rational numbers also. The rational numbers are −3, −2, −1.5, 0, , 11, and 112.

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e. The irrational number is .

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f. The real numbers are all numbers in the given set.