Determine which numbers are a. natural numbers, b. whole...

Determine which numbers are
a. natural numbers,
b. whole numbers,
c. integers,
d. rational numbers, and
e. irrational numbers.
$$\left\{25,-17,-\frac{12}{5}, \sqrt{9}, 3.12, \frac{1}{2} \pi, 6,-4,18\right\}$$

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Key Concepts

Irrational Numbers

Irrational numbers cannot be expressed as the quotient of two integers and have non-terminating, non-repeating decimal representations. They often result from square roots of non-perfect squares or specific constants such as ?.

Rational Numbers

Rational numbers are those that can be expressed as the quotient of two integers, where the denominator is not zero. This includes integers (which can be written as a fraction with denominator one), fractions, and decimals that terminate or repeat.

Integers

Integers extend whole numbers by including their negative counterparts. This set encompasses all positive numbers, zero, and negative numbers, forming a complete set of whole number values in both directions.

Whole Numbers

Whole numbers include all natural numbers along with zero. They form the set of non-negative integers, excluding any negative numbers or fractional values.

Natural Numbers

Natural numbers are the positive counting numbers typically starting from 1. They are used for counting and ordering, and they do not include zero, negative numbers, fractions, or decimals.

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