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

list the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers.
$$
A=\left\{-6, \frac{1}{2},-1.333 \ldots\left(\text { the } 3^{\prime} \text { 's repeat }\right), \pi, 2,5\right\}
$$

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Key Concepts

Irrational Numbers

Irrational numbers are numbers that cannot be expressed as a fraction of two integers. Their decimal representations are non-terminating and non-repeating, and examples include certain roots and transcendental numbers.

Rational Numbers

Rational numbers are numbers that can be expressed as a fraction of two integers where the denominator is not zero. This set includes integers (since any integer can be written as a fraction with denominator 1) as well as fractions and terminating or repeating decimals.

Real Numbers

Real numbers include all the numbers that can be found on the number line, encompassing both rational and irrational numbers. They represent a complete and continuous set without any gaps.

Natural Numbers

Natural numbers are the counting numbers typically starting from 1 and increasing without bound. They are used to count objects and do not include zero, negative numbers, fractions, or decimals.

Integers

Integers consist of all whole numbers, including negative whole numbers, zero, and positive whole numbers. They form a set that is closed under addition, subtraction, and multiplication.

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