List the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (

step 1 So our natural numbers are the numbers we use to count with. So no negatives, no zero, and no fr

List the numbers in each set that are (a) Natural numbers,...

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Key Concepts

Real Numbers

Real numbers encompass all the numbers that can be found on the number line, including both rational and irrational numbers. They represent all possible magnitudes and can be described by either finite or infinite decimal expansions, covering every point on the continuum.

Irrational Numbers

Irrational numbers are real numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are non-terminating and non-repeating, meaning they cannot be exactly expressed in fractional form. Common examples include certain roots and transcendental numbers.

Integers

Integers comprise the set of whole numbers that include positive numbers, zero, and negative numbers. This set does not include any numbers with fractional or decimal parts, and it is often denoted as {..., -3, -2, -1, 0, 1, 2, 3, ...}.

Rational Numbers

Rational numbers are those numbers that can be expressed as the quotient or fraction of two integers, where the divisor is not zero. This set includes integers, finite decimals, and repeating decimals, and it provides a way to represent numbers as ratios.

Natural Numbers

Natural numbers are the set of positive integers typically used for counting. They usually begin with 1 and continue upward (1, 2, 3, ...), and do not include zero, negative numbers, or any fractional or decimal values.

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