For each set, list all elements that belong to the (a)...

For each set, list all elements that belong to the
(a) natural numbers
(b) whole numbers
(c) integers
(d) rational numbers
(e) irrational numbers
(f) real numbers
$$\left\{-8,-\frac{14}{7},-0.245,0, \frac{6}{2}, 8, \sqrt{81}, \sqrt{12}\right\}$$

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Key Concepts

Irrational Numbers

Irrational numbers cannot be expressed as a ratio of two integers and have non-terminating, non-repeating decimal expansions. They fill the gaps between rational numbers on the real number line.

Real Numbers

Real numbers consist of both rational and irrational numbers, forming a complete set that includes every point on the number line. They are the foundation of real analysis and include all numbers that can be represented as decimals, whether terminating, repeating, or non-repeating.

Rational Numbers

Rational numbers are numbers that can be expressed as the fraction of two integers, where the denominator is not zero. They include both terminating decimals and repeating decimals, and they encompass integers as well.

Whole Numbers

Whole numbers consist of all natural numbers along with zero, forming a set that includes 0, 1, 2, 3, and so on. They are useful in contexts where the concept of 'nothing' (zero) is meaningful alongside counting numbers.

Natural Numbers

Natural numbers are the set of positive integers typically used for counting. They generally start at 1 and continue indefinitely (1, 2, 3, ...).

Integers

Integers are the set of whole numbers and their negatives. This set includes ..., -3, -2, -1, 0, 1, 2, 3, and continues infinitely in both the positive and negative directions.

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